1
|
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.
Collapse
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
| |
Collapse
|
2
|
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.
Collapse
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.)
| |
Collapse
|
3
|
Baity-Jesi M, Baños RA, Cruz A, Fernandez LA, Gil-Narvion JM, Gordillo-Guerrero A, Iñiguez D, Maiorano A, Mantovani F, Marinari E, Martin-Mayor V, Monforte-Garcia J, Muñoz Sudupe A, Navarro D, Parisi G, Perez-Gaviro S, Pivanti M, Ricci-Tersenghi F, Ruiz-Lorenzo JJ, Schifano SF, Seoane B, Tarancon A, Tripiccione R, Yllanes D. Dynamical transition in the D=3 Edwards-Anderson spin glass in an external magnetic field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032140. [PMID: 24730822 DOI: 10.1103/physreve.89.032140] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2013] [Indexed: 06/03/2023]
Abstract
We study the off-equilibrium dynamics of the three-dimensional Ising spin glass in the presence of an external magnetic field. We have performed simulations both at fixed temperature and with an annealing protocol. Thanks to the Janus special-purpose computer, based on field-programmable gate array (FPGAs), we have been able to reach times equivalent to 0.01 s in experiments. We have studied the system relaxation both for high and for low temperatures, clearly identifying a dynamical transition point. This dynamical temperature is strictly positive and depends on the external applied magnetic field. We discuss different possibilities for the underlying physics, which include a thermodynamical spin-glass transition, a mode-coupling crossover, or an interpretation reminiscent of the random first-order picture of structural glasses.
Collapse
Affiliation(s)
- M Baity-Jesi
- Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain and Dipartimento di Fisica, La Sapienza Università di Roma, 00185 Roma, Italy and Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| | - R A Baños
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain and Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain
| | - A Cruz
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain and Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain
| | - L A Fernandez
- Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain and Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| | - J M Gil-Narvion
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| | - A Gordillo-Guerrero
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain and D. de Ingeniería Eléctrica, Electrónica y Automática, U. de Extremadura, 10071, Cáceres, Spain
| | - D Iñiguez
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain and Fundación ARAID, Diputación General de Aragón, Zaragoza, Spain
| | - A Maiorano
- Dipartimento di Fisica, La Sapienza Università di Roma, 00185 Roma, Italy and Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| | - F Mantovani
- Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, and INFN, Ferrara, Italy
| | - E Marinari
- Dipartimento di Fisica, IPCF-CNR, UOS Roma Kerberos and INFN, La Sapienza Università di Roma, 00185 Roma, Italy
| | - V Martin-Mayor
- Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain and Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| | - J Monforte-Garcia
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain and Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain
| | - A Muñoz Sudupe
- Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
| | - D Navarro
- D. de Ingeniería, Electrónica y Comunicaciones and I3A, U. de Zaragoza, 50018 Zaragoza, Spain
| | - G Parisi
- Dipartimento di Fisica, IPCF-CNR, UOS Roma Kerberos and INFN, La Sapienza Università di Roma, 00185 Roma, Italy
| | - S Perez-Gaviro
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain and Fundación ARAID, Diputación General de Aragón, Zaragoza, Spain
| | - M Pivanti
- Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, and INFN, Ferrara, Italy
| | - F Ricci-Tersenghi
- Dipartimento di Fisica, IPCF-CNR, UOS Roma Kerberos and INFN, La Sapienza Università di Roma, 00185 Roma, Italy
| | - J J Ruiz-Lorenzo
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain and Departamento de Física, Universidad de Extremadura, 06071 Badajoz, Spain
| | - S F Schifano
- Dipartimento di Matematica e Informatica, Università di Ferrara and INFN, Ferrara, Italy
| | - B Seoane
- Dipartimento di Fisica, La Sapienza Università di Roma, 00185 Roma, Italy and Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| | - A Tarancon
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain and Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain
| | - R Tripiccione
- Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, and INFN, Ferrara, Italy
| | - D Yllanes
- Dipartimento di Fisica, La Sapienza Università di Roma, 00185 Roma, Italy and Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
| |
Collapse
|
4
|
Billoire A, Coluzzi B. Numerical study of the Sherrington-Kirkpatrick model in a magnetic field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:026131. [PMID: 14525073 DOI: 10.1103/physreve.68.026131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2003] [Indexed: 05/24/2023]
Abstract
We study numerically the Sherrington-Kirkpatrick model as a function of the magnetic field h, with fixed temperature T=0.6T(c). We investigate the finite size scaling behavior of several quantities, such as the spin-glass susceptibility, searching for numerical evidences of the transition on the de Almeida-Thouless line. We find strong corrections to scaling which make difficult to locate the transition point. This shows, in a simple case, the extreme difficulties of spin-glass simulations in a nonzero magnetic field. Next, we study various sum rules (consequences of stochastic stability) involving overlaps between three and four replicas, which appear to be numerically well satisfied, and in a nontrivial way. Finally, we present data on P(q) for a large lattice size (N=3200) at low temperature T=0.4T(c), where the shape predicted by the replica symmetry breaking solution of the model for a nonzero magnetic field is visible.
Collapse
Affiliation(s)
- Alain Billoire
- Service de Physique Théorique, CEA-Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette, France
| | | |
Collapse
|
5
|
Temesvári T, De Dominicis C. Replica field theory and renormalization group for the Ising spin glass in an external magnetic field. PHYSICAL REVIEW LETTERS 2002; 89:097204. [PMID: 12190434 DOI: 10.1103/physrevlett.89.097204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2002] [Indexed: 05/23/2023]
Abstract
We use the generic replica symmetric cubic field theory to study the transition of short-range Ising spin glasses in a magnetic field around the upper critical dimension. A novel fixed point is found from the application of the renormalization group. In the spin-glass limit, this fixed point governs the critical behavior of a class of systems characterized by a single cubic parameter. For this universality class, the spin-glass susceptibility diverges at criticality, whereas the longitudinal mode remains massive. The third mode, however, behaves unusually. The physical consequences of this unusual behavior are discussed, and a comparison with the conventional de Almeida-Thouless scenario is presented.
Collapse
Affiliation(s)
- T Temesvári
- HAS Research Group for Theoretical Physics, Eötvös University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary.
| | | |
Collapse
|
6
|
Krzakala F, Houdayer J, Marinari E, Martin OC, Parisi G. Zero-temperature responses of a 3D spin glass in a magnetic field. PHYSICAL REVIEW LETTERS 2001; 87:197204. [PMID: 11690454 DOI: 10.1103/physrevlett.87.197204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2001] [Indexed: 05/23/2023]
Abstract
We probe the energy landscape of the 3D Edwards-Anderson spin glass in a magnetic field to test for a spin glass ordering. We find that the spin glass susceptibility is anomalously large on the lattice sizes we can reach. Our data suggest that a transition from the spin glass to the paramagnetic phase takes place at B(c) approximately 0.65, though the possibility B(c) = 0 cannot be excluded. We also discuss the question of the nature of the putative frozen phase.
Collapse
Affiliation(s)
- F Krzakala
- Laboratoire de Physique Théorique et Modèles Statistiques, bât. 100, Université Paris-Sud, F-91405 Orsay, France
| | | | | | | | | |
Collapse
|
7
|
Barrat A, Berthier L. Real-space application of the mean-field description of spin-glass dynamics. PHYSICAL REVIEW LETTERS 2001; 87:087204. [PMID: 11497979 DOI: 10.1103/physrevlett.87.087204] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2001] [Indexed: 05/23/2023]
Abstract
The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard "mean-field theory" versus "droplet picture" debate of the past decades. The main predictions of both theories concerning the spin-glass dynamics are discussed. It is shown, in particular, that predictions originating from mean-field ideas concerning the violations of the fluctuation-dissipation theorem apply quantitatively, provided one properly takes into account the role of a spin-glass coherence length, which plays a central role in the droplet picture. Dynamics in a uniform magnetic field is also briefly discussed.
Collapse
Affiliation(s)
- A Barrat
- Laboratoire de Physique Théorique, Bâtiment 210, Université de Paris-Sud, 91405 Orsay Cedex, France
| | | |
Collapse
|
8
|
Marinari E, Parisi G, Ricci-Tersenghi F, Ruiz-Lorenzo JJ. Off-equilibrium dynamics at very low temperatures in three-dimensional spin glasses. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0305-4470/33/12/305] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
9
|
Marinari E, Parisi G, Zuliani F. Comment on "ising spin glasses in a magnetic field". PHYSICAL REVIEW LETTERS 2000; 84:1056-1057. [PMID: 11017440 DOI: 10.1103/physrevlett.84.1056] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/1999] [Indexed: 05/23/2023]
|
10
|
Marinari E, Naitza C, Zuliani F. Critical behaviour of the four-dimensional spin glass in magnetic field. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/31/30/005] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|