1
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Aguilar-Janita M, Martin-Mayor V, Moreno-Gordo J, Ruiz-Lorenzo JJ. Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field. Phys Rev E 2024; 109:055302. [PMID: 38907467 DOI: 10.1103/physreve.109.055302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2023] [Accepted: 04/05/2024] [Indexed: 06/24/2024]
Abstract
The very existence of a phase transition for spin glasses in an external magnetic field is controversial, even in high dimensions. We carry out massive simulations of the Ising spin-glass in a field, in six dimensions (which, according to classical-but not generally accepted-field-theoretical studies, is the upper critical dimension). We obtain results compatible with a second-order phase transition and estimate its critical exponents for the simulated lattice sizes. The detailed analysis performed by other authors of the replica symmetric Hamiltonian, under the hypothesis of critical behavior, predicts that the ratio of the renormalized coupling constants remain bounded as the correlation length grows. Our numerical results are in agreement with this expectation.
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Affiliation(s)
- M Aguilar-Janita
- Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
| | - V Martin-Mayor
- Departamento de Física Teórica, Universidad Complutense, 28040 Madrid, Spain and Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain
| | - J Moreno-Gordo
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain; Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain; Departamento de Física, Universidad de Extremadura, 06006 Badajoz, Spain; and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06006 Badajoz, Spain
| | - J J Ruiz-Lorenzo
- Departamento de Física, Universidad de Extremadura, 06006 Badajoz, Spain; Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06006 Badajoz, Spain; and Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain
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2
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Fernandez LA, Gonzalez-Adalid Pemartin I, Martin-Mayor V, Parisi G, Ricci-Tersenghi F, Rizzo T, Ruiz-Lorenzo JJ, Veca M. Numerical test of the replica-symmetric Hamiltonian for correlations of the critical state of spin glasses in a field. Phys Rev E 2022; 105:054106. [PMID: 35706223 DOI: 10.1103/physreve.105.054106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Accepted: 03/28/2022] [Indexed: 06/15/2023]
Abstract
A growing body of evidence indicates that the sluggish low-temperature dynamics of glass formers (e.g., supercooled liquids, colloids, or spin glasses) is due to a growing correlation length. Which is the effective field theory that describes these correlations? The natural field theory was drastically simplified by Bray and Roberts in 1980. More than 40 years later, we confirm the tenets of Bray and Roberts's theory by studying the Ising spin glass in an externally applied magnetic field, both in four spatial dimensions (data obtained from the Janus collaboration) and on the Bethe lattice.
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Affiliation(s)
- L A Fernandez
- Departamento de Física Teórica, Universidad Complutense, 28040 Madrid, Spain
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain
| | | | - V Martin-Mayor
- Departamento de Física Teórica, Universidad Complutense, 28040 Madrid, Spain
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain
| | - G Parisi
- Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 5, 00185 Rome, Italy
- INFN, Sezione di Roma 1, P.le A. Moro 5, 00185 Rome, Italy
- CNR-Nanotec, Unità di Roma, P.le A. Moro 5, 00185 Rome, Italy
| | - F Ricci-Tersenghi
- Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 5, 00185 Rome, Italy
- INFN, Sezione di Roma 1, P.le A. Moro 5, 00185 Rome, Italy
- CNR-Nanotec, Unità di Roma, P.le A. Moro 5, 00185 Rome, Italy
| | - T Rizzo
- Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 5, 00185 Rome, Italy
- Institute of Complex Systems (ISC) - CNR, Rome Unit, P.le A. Moro 5, 00185 Rome, Italy
| | - J J Ruiz-Lorenzo
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain
- Departamento de Física, Universidad de Extremadura, 06006 Badajoz, Spain
- Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06006 Badajoz, Spain
| | - M Veca
- Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 5, 00185 Rome, Italy
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3
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Angelini MC, Lucibello C, Parisi G, Perrupato G, Ricci-Tersenghi F, Rizzo T. Unexpected Upper Critical Dimension for Spin Glass Models in a Field Predicted by the Loop Expansion around the Bethe Solution at Zero Temperature. PHYSICAL REVIEW LETTERS 2022; 128:075702. [PMID: 35244416 DOI: 10.1103/physrevlett.128.075702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Revised: 01/18/2022] [Accepted: 01/26/2022] [Indexed: 06/14/2023]
Abstract
The spin-glass transition in a field in finite dimension is analyzed directly at zero temperature using a perturbative loop expansion around the Bethe lattice solution. The loop expansion is generated by the M-layer construction whose first diagrams are evaluated numerically and analytically. The generalized Ginzburg criterion reveals that the upper critical dimension below which mean-field theory fails is D_{U}≥8, at variance with the classical result D_{U}=6 yielded by finite-temperature replica field theory. Our expansion around the Bethe lattice has two crucial differences with respect to the classical one. The finite connectivity z of the lattice is directly included from the beginning in the Bethe lattice, while in the classical computation the finite connectivity is obtained through an expansion in 1/z. Moreover, if one is interested in the zero temperature (T=0) transition, one can directly expand around the T=0 Bethe transition. The expansion directly at T=0 is not possible in the classical framework because the fully connected spin glass does not have a transition at T=0, being in the broken phase for any value of the external field.
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Affiliation(s)
- Maria Chiara Angelini
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Rome, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, Piazzale Aldo Moro 5, 00185 Rome, Italy
| | - Carlo Lucibello
- Bocconi Institute for Data Science and Analytics (BIDSA), Bocconi University, Via Sarfatti 25, 20100 Milan, Italy
| | - Giorgio Parisi
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Rome, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, Piazzale Aldo Moro 5, 00185 Rome, Italy
- Institute of Nanotechnology (NANOTEC)-CNR, Rome unit, Piazzale Aldo Moro 5, 00185 Rome, Italy
| | - Gianmarco Perrupato
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Rome, Italy
| | - Federico Ricci-Tersenghi
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Rome, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, Piazzale Aldo Moro 5, 00185 Rome, Italy
- Institute of Nanotechnology (NANOTEC)-CNR, Rome unit, Piazzale Aldo Moro 5, 00185 Rome, Italy
| | - Tommaso Rizzo
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Rome, Italy
- Institute of Complex Systems (ISC)-CNR, Rome unit, Piazzale Aldo Moro 5, 00185 Rome, Italy
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4
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Zhang D, Chen T, Vucelja M, Lee SH, Chern GW. Memory effect and phase transition in a hierarchical trap model for spin glasses. Phys Rev E 2021; 104:064105. [PMID: 35030869 DOI: 10.1103/physreve.104.064105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2018] [Accepted: 11/18/2021] [Indexed: 06/14/2023]
Abstract
We introduce an efficient dynamical tree method that enables us to explicitly demonstrate the thermoremanent magnetization memory effect in a hierarchical energy landscape. Our simulation nicely reproduces the nontrivial waiting-time and waiting-temperature dependences in this nonequilibrium phenomenon. We further investigate the condensation effect, in which a small set of microstates dominates the thermodynamic behavior in the multilayer trap model. Importantly, a structural phase transition of the multilayer tree model is shown to coincide with the onset of the condensation phenomenon. Our results underscore the importance of hierarchical structure and demonstrate the intimate relation between the glassy behavior and structure of barrier trees.
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Affiliation(s)
- Depei Zhang
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Tianran Chen
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Marija Vucelja
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Seung-Hun Lee
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Gia-Wei Chern
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
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5
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Albert S, Biroli G, Ladieu F, Tourbot R, Urbani P. Searching for the Gardner Transition in Glassy Glycerol. PHYSICAL REVIEW LETTERS 2021; 126:028001. [PMID: 33512182 DOI: 10.1103/physrevlett.126.028001] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2020] [Accepted: 12/21/2020] [Indexed: 06/12/2023]
Abstract
We search for a Gardner transition in glassy glycerol, a standard molecular glass, measuring the third harmonics cubic susceptibility χ_{3}^{(3)} from slightly below the usual glass transition temperature down to 10 K. According to the mean-field picture, if local motion within the glass were becoming highly correlated due to the emergence of a Gardner phase then χ_{3}^{(3)}, which is analogous to the dynamical spin-glass susceptibility, should increase and diverge at the Gardner transition temperature T_{G}. We find instead that upon cooling |χ_{3}^{(3)}| decreases by several orders of magnitude and becomes roughly constant in the regime 100-10 K. We rationalize our findings by assuming that the low temperature physics is described by localized excitations weakly interacting via a spin-glass dipolar pairwise interaction in a random magnetic field. Our quantitative estimations show that the spin-glass interaction is twenty to fifty times smaller than the local random field contribution, thus rationalizing the absence of the spin-glass Gardner phase. This hints at the fact that a Gardner phase may be suppressed in standard molecular glasses, but it also suggests ways to favor its existence in other amorphous solids and by changing the preparation protocol.
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Affiliation(s)
- Samuel Albert
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay Bâtiment 772, 91191 Gif-sur-Yvette Cedex, France
| | - Giulio Biroli
- Laboratoire de Physique de l'Ecole normale supérieure ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, 75005 Sorbonne Paris Cité, Paris, France
| | - François Ladieu
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay Bâtiment 772, 91191 Gif-sur-Yvette Cedex, France
| | - Roland Tourbot
- SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay Bâtiment 772, 91191 Gif-sur-Yvette Cedex, France
| | - Pierfrancesco Urbani
- Université Paris-Saclay, CNRS, CEA, Institut de Physique Théorique, 91191 Gif-sur-Yvette, France
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6
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Fang C, Barzeger A, Katzgraber HG. Machine learning in physics: the pitfalls of poisoned training sets. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2020. [DOI: 10.1088/2632-2153/aba821] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
Abstract
Known for their ability to identify hidden patterns in data, artificial neural networks are among the most powerful machine learning tools. Most notably, neural networks have played a central role in identifying states of matter and phase transitions across condensed matter physics. To date, most studies have focused on systems where different phases of matter and their phase transitions are known, and thus the performance of neural networks is well controlled. While neural networks present an exciting new tool to detect new phases of matter, here we demonstrate that when the training sets are poisoned (i.e. poor training data or mislabeled data) it is easy for neural networks to make misleading predictions.
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7
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Höller J, Read N. One-step replica-symmetry-breaking phase below the de Almeida-Thouless line in low-dimensional spin glasses. Phys Rev E 2020; 101:042114. [PMID: 32422847 DOI: 10.1103/physreve.101.042114] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2019] [Accepted: 03/16/2020] [Indexed: 06/11/2023]
Abstract
The de Almeida-Thouless (AT) line is the phase boundary in the temperature-magnetic field plane of an Ising spin glass at which a continuous (i.e., second-order) transition from a paramagnet to a replica-symmetry-breaking (RSB) phase occurs, according to mean-field theory. Here, using field-theoretic perturbative renormalization group methods on the Bray-Roberts reduced Landau-Ginzburg-type theory for a short-range Ising spin glass in space of dimension d, we show that at nonzero magnetic field the nature of the corresponding transition is modified as follows: (a) For d-6 small and positive, with increasing field on the AT line, first, the ordered phase just below the transition becomes the so-called one-step RSB, instead of the full RSB that occurs in mean-field theory; the transition on the AT line remains continuous with a diverging correlation length. Then at a higher field, a tricritical point separates the latter transition from a quasi-first-order one, that is one at which the correlation length does not diverge, and there is a jump in part of the order parameter, but no latent heat. The location of the tricritical point tends to zero as d→6^{+}. (b) For d≤6, we argue that the quasi-first-order transition could persist down to arbitrarily small nonzero fields, with a transition to full RSB still expected at lower temperature. Whenever the quasi-first-order transition occurs, it is at a higher temperature than the AT transition would be for the same field, preempting it as the temperature is lowered. These results may explain the reported absence of a diverging correlation length in the presence of a magnetic field in low-dimensional spin glasses in some simulations and in high-temperature series expansions. We also draw attention to the similarity of the "dynamically frozen" state, which occurs at temperatures just above the quasi-first-order transition, and the "metastate-average state" of the one-step RSB phase, and discuss the issue of the number of pure states in either.
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Affiliation(s)
- J Höller
- Department of Physics, Yale University, P.O. Box 208120, New Haven, Connecticut 06520-8120, USA
| | - N Read
- Department of Physics, Yale University, P.O. Box 208120, New Haven, Connecticut 06520-8120, USA
- Department of Applied Physics, Yale University, P.O. Box 208284, New Haven, Connecticut 06520-8284, USA
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8
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Dilucca M, Leuzzi L, Parisi G, Ricci-Tersenghi F, Ruiz-Lorenzo JJ. Spin Glasses in a Field Show a Phase Transition Varying the Distance among Real Replicas (And How to Exploit It to Find the Critical Line in a Field). ENTROPY 2020; 22:e22020250. [PMID: 33286024 PMCID: PMC7516687 DOI: 10.3390/e22020250] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Revised: 02/18/2020] [Accepted: 02/20/2020] [Indexed: 11/16/2022]
Abstract
We discuss a phase transition in spin glass models that have been rarely considered in the past, namely, the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e., at a smaller overlap) than the typical one. In the first part of the work, by solving analytically the Sherrington-Kirkpatrick model in a field close to its critical point, we show that, even in a paramagnetic phase, the forcing of two real replicas to an overlap small enough leads the model to a phase transition where the symmetry between replicas is spontaneously broken. More importantly, this phase transition is related to the de Almeida-Thouless (dAT) critical line. In the second part of the work, we exploit the phase transition in the overlap between two real replicas to identify the critical line in a field in finite dimensional spin glasses. This is a notoriously difficult computational problem, because of considerable finite size corrections. We introduce a new method of analysis of Monte Carlo data for disordered systems, where the overlap between two real replicas is used as a conditioning variate. We apply this analysis to equilibrium measurements collected in the paramagnetic phase in a field, h > 0 and T c ( h ) < T < T c ( h = 0 ) , of the d = 1 spin glass model with long range interactions decaying fast enough to be outside the regime of validity of the mean field theory. We thus provide very reliable estimates for the thermodynamic critical temperature in a field.
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Affiliation(s)
- Maddalena Dilucca
- Dipartimento di Fisica, Sapienza Universitá di Roma, P.le A. Moro 2, I-00185 Roma, Italy;
| | - Luca Leuzzi
- Dipartimento di Fisica, Sapienza Universitá di Roma, P.le A. Moro 2, I-00185 Roma, Italy;
- CNR, Nanotec, Rome unit, P.le A. Moro 2, I-00185 Roma, Italy
- Correspondence: (L.L.); (G.P.); (F.R.-T.); (J.J.R.-L.)
| | - Giorgio Parisi
- Dipartimento di Fisica, Sapienza Universitá di Roma, P.le A. Moro 2, I-00185 Roma, Italy;
- CNR, Nanotec, Rome unit, P.le A. Moro 2, I-00185 Roma, Italy
- INFN, Sezione di Roma I, P.le A. Moro 2, I-00185 Roma, Italy
- Correspondence: (L.L.); (G.P.); (F.R.-T.); (J.J.R.-L.)
| | - Federico Ricci-Tersenghi
- Dipartimento di Fisica, Sapienza Universitá di Roma, P.le A. Moro 2, I-00185 Roma, Italy;
- CNR, Nanotec, Rome unit, P.le A. Moro 2, I-00185 Roma, Italy
- INFN, Sezione di Roma I, P.le A. Moro 2, I-00185 Roma, Italy
- Correspondence: (L.L.); (G.P.); (F.R.-T.); (J.J.R.-L.)
| | - Juan J. Ruiz-Lorenzo
- Departamendo de Física and ICCAEx, Universidad de Extremadura, 06006 Badajoz, Spain
- Instituto de Biocomputación y Física de los Sistemas Complejos (BIFI), 50018 Zaragoza, Spain
- Correspondence: (L.L.); (G.P.); (F.R.-T.); (J.J.R.-L.)
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9
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Charbonneau P, Hu Y, Raju A, Sethna JP, Yaida S. Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class. Phys Rev E 2019; 99:022132. [PMID: 30934357 DOI: 10.1103/physreve.99.022132] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2018] [Indexed: 11/07/2022]
Abstract
A replica-symmetry-breaking phase transition is predicted in a host of disordered media. The criticality of the transition has, however, long been questioned below its upper critical dimension, six, due to the absence of a critical fixed point in the renormalization-group flows at one-loop order. A recent two-loop analysis revealed a possible strong-coupling fixed point, but given the uncontrolled nature of perturbative analysis in the strong-coupling regime, debate persists. Here we examine the nature of the transition as a function of spatial dimension and show that the strong-coupling fixed point can go through a Hopf bifurcation, resulting in a critical limit cycle and a concomitant discrete scale invariance. We further investigate a different renormalization scheme and argue that the basin of attraction of the strong-coupling fixed point (or limit cycle) may stay finite for all dimensions.
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Affiliation(s)
- Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.,Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Yi Hu
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Archishman Raju
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
| | - James P Sethna
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
| | - Sho Yaida
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
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10
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Seoane B, Zamponi F. Spin-glass-like aging in colloidal and granular glasses. SOFT MATTER 2018; 14:5222-5234. [PMID: 29892754 DOI: 10.1039/c8sm00859k] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Motivated by the mean field prediction of a Gardner phase transition between a "normal glass" and a "marginally stable glass", we investigate the off-equilibrium dynamics of three-dimensional polydisperse hard spheres, used as a model for colloidal or granular glasses. Deep inside the glass phase, we find that a sharp crossover pressure PG separates two distinct dynamical regimes. For pressure P < PG, the glass behaves as a normal solid, displaying fast dynamics that quickly equilibrate within the glass free energy basin. For P > PG, instead, the dynamics become strongly anomalous, displaying very large equilibration timescales, aging, and a constantly increasing dynamical susceptibility. The crossover at PG is strongly reminiscent of the one observed in three-dimensional spin-glasses in an external field, suggesting that the two systems could be in the same universality class, consistent with theoretical expectations.
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Affiliation(s)
- Beatriz Seoane
- Laboratoire de physique théorique, Département de physique de l'ENS, École normale supérieure, PSL Research University, Sorbonne Universités, CNRS, 75005 Paris, France
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11
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Hicks CL, Wheatley MJ, Godfrey MJ, Moore MA. Gardner Transition in Physical Dimensions. PHYSICAL REVIEW LETTERS 2018; 120:225501. [PMID: 29906167 DOI: 10.1103/physrevlett.120.225501] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2017] [Revised: 01/19/2018] [Indexed: 06/08/2023]
Abstract
The Gardner transition is the transition that at mean-field level separates a stable glass phase from a marginally stable phase. This transition has similarities with the de Almeida-Thouless transition of spin glasses. We have studied a well-understood problem, that of disks moving in a narrow channel, which shows many features usually associated with the Gardner transition. We show that some of these features are artifacts that arise when a disk escapes its local cage during the quench to higher densities. There is evidence that the Gardner transition becomes an avoided transition, in that the correlation length becomes quite large, of order 15 particle diameters, even in our quasi-one-dimensional system.
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Affiliation(s)
- C L Hicks
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
| | - M J Wheatley
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
| | - M J Godfrey
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
| | - M A Moore
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
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12
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Moore MA, Read N. Multicritical Point on the de Almeida-Thouless Line in Spin Glasses in d>6 Dimensions. PHYSICAL REVIEW LETTERS 2018; 120:130602. [PMID: 29694168 DOI: 10.1103/physrevlett.120.130602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2018] [Indexed: 06/08/2023]
Abstract
The de Almeida-Thouless (AT) line in Ising spin glasses is the phase boundary in the temperature T and magnetic field h plane below which replica symmetry is broken. Using perturbative renormalization group (RG) methods, we show that, when the dimension d of space is just above six, there is a multicritical point (MCP) on the AT line, which separates a low-field regime, in which the critical exponents have mean-field values, from a high-field regime, where the RG flows run away to infinite coupling strength; as d approaches six from above, the MCP approaches the zero-field critical point exponentially in 1/(d-6). Thus, on the AT line, perturbation theory for the critical properties breaks down at a sufficiently large magnetic field even above 6 dimensions, as well as for all nonzero fields when d≤6, as was known previously. We calculate the exponents at the MCP to first order in ϵ=d-6>0. The fate of the MCP as d increases from just above six to infinity is not known.
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Affiliation(s)
- M A Moore
- School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
| | - N Read
- Department of Physics, Yale University, P.O. Box 208120, New Haven, Connecticut 06520-8120, USA
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13
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Procaccia I, Rainone C, Singh M. Mechanical failure in amorphous solids: Scale-free spinodal criticality. Phys Rev E 2017; 96:032907. [PMID: 29346984 DOI: 10.1103/physreve.96.032907] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2017] [Indexed: 06/07/2023]
Abstract
The mechanical failure of amorphous media is a ubiquitous phenomenon from material engineering to geology. It has been noticed for a long time that the phenomenon is "scale-free," indicating some type of criticality. In spite of attempts to invoke "Self-Organized Criticality," the physical origin of this criticality, and also its universal nature, being quite insensitive to the nature of microscopic interactions, remained elusive. Recently we proposed that the precise nature of this critical behavior is manifested by a spinodal point of a thermodynamic phase transition. Demonstrating this requires the introduction of an "order parameter" that is suitable for distinguishing between disordered amorphous systems. At the spinodal point there exists a divergent correlation length which is associated with the system-spanning instabilities (known also as shear bands) which are typical to the mechanical yield. The theory, the order parameter used and the correlation functions which exhibit the divergent correlation length are universal in nature and can be applied to any amorphous solid that undergoes mechanical yield. The phenomenon is seen at its sharpest in athermal systems, as is explained below; in this paper we extend the discussion also to thermal systems, showing that at sufficiently high temperatures the spinodal phenomenon is destroyed by thermal fluctuations.
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Affiliation(s)
- Itamar Procaccia
- Department of Chemical Physics, the Weizmann Institute of Science, Rehovot 76100, Israel
| | - Corrado Rainone
- Department of Chemical Physics, the Weizmann Institute of Science, Rehovot 76100, Israel
| | - Murari Singh
- Department of Chemical Physics, the Weizmann Institute of Science, Rehovot 76100, Israel
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14
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Parisi G, Procaccia I, Rainone C, Singh M. Shear bands as manifestation of a criticality in yielding amorphous solids. Proc Natl Acad Sci U S A 2017; 114:5577-5582. [PMID: 28512221 PMCID: PMC5465875 DOI: 10.1073/pnas.1700075114] [Citation(s) in RCA: 66] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Amorphous solids increase their stress as a function of an applied strain until a mechanical yield point whereupon the stress cannot increase anymore, afterward exhibiting a steady state with a constant mean stress. In stress-controlled experiments, the system simply breaks when pushed beyond this mean stress. The ubiquity of this phenomenon over a huge variety of amorphous solids calls for a generic theory that is free of microscopic details. Here, we offer such a theory: The mechanical yield is a thermodynamic phase transition, where yield occurs as a spinodal phenomenon. At the spinodal point, there exists a divergent correlation length that is associated with the system-spanning instabilities (also known as shear bands), which are typical to the mechanical yield. The theory, the order parameter used, and the correlation functions that exhibit the divergent correlation length are universal in nature and can be applied to any amorphous solids that undergo mechanical yield.
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Affiliation(s)
- Giorgio Parisi
- Dipartimento di Fisica, Sapienza Universitá di Roma, Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, Istituto per i Processi Chimico-Fisici (IPCF)-Consiglio Nazionale delle Ricerche, I-00185 Rome, Italy;
| | - Itamar Procaccia
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Corrado Rainone
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
| | - Murari Singh
- Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel
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15
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Charbonneau P, Jin Y, Parisi G, Rainone C, Seoane B, Zamponi F. Numerical detection of the Gardner transition in a mean-field glass former. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012316. [PMID: 26274170 DOI: 10.1103/physreve.92.012316] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2015] [Indexed: 06/04/2023]
Abstract
Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.
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Affiliation(s)
- Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
| | - Yuliang Jin
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Dipartimento di Fisica, Sapienza Universitá di Roma, INFN, Sezione di Roma I, IPFC - CNR, Piazzale Aldo Moro 2, I-00185 Roma, Italy
- LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France
| | - Giorgio Parisi
- Dipartimento di Fisica, Sapienza Universitá di Roma, INFN, Sezione di Roma I, IPFC - CNR, Piazzale Aldo Moro 2, I-00185 Roma, Italy
| | - Corrado Rainone
- Dipartimento di Fisica, Sapienza Universitá di Roma, INFN, Sezione di Roma I, IPFC - CNR, Piazzale Aldo Moro 2, I-00185 Roma, Italy
- LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France
| | - Beatriz Seoane
- Dipartimento di Fisica, Sapienza Universitá di Roma, INFN, Sezione di Roma I, IPFC - CNR, Piazzale Aldo Moro 2, I-00185 Roma, Italy
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| | - Francesco Zamponi
- LPT, École Normale Supérieure, UMR 8549 CNRS, 24 Rue Lhomond, 75005 Paris, France
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16
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Angelini MC, Biroli G. Spin glass in a field: a new zero-temperature fixed point in finite dimensions. PHYSICAL REVIEW LETTERS 2015; 114:095701. [PMID: 25793828 DOI: 10.1103/physrevlett.114.095701] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2014] [Indexed: 06/04/2023]
Abstract
By using real-space renormalization group (RG) methods, we show that spin glasses in a field display a new kind of transition in high dimensions. The corresponding critical properties and the spin-glass phase are governed by two nonperturbative zero-temperature fixed points of the RG flow. We compute the critical exponents and discuss the RG flow and its relevance for three-dimensional systems. The new spin-glass phase we discovered has unusual properties, which are intermediate between the ones conjectured by droplet and full replica symmetry-breaking theories. These results provide a new perspective on the long-standing debate about the behavior of spin glasses in a field.
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Affiliation(s)
- Maria Chiara Angelini
- Institut de Physique Théorique, CEA/DSM/IPhT-CNRS/URA 2306 CEA-Saclay, F-91191 Gif-sur-Yvette, France
| | - Giulio Biroli
- Institut de Physique Théorique, CEA/DSM/IPhT-CNRS/URA 2306 CEA-Saclay, F-91191 Gif-sur-Yvette, France
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