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Franz S, Gradenigo G, Spigler S. Random-diluted triangular plaquette model: Study of phase transitions in a kinetically constrained model. Phys Rev E 2016; 93:032601. [PMID: 27078408 DOI: 10.1103/physreve.93.032601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2015] [Indexed: 11/07/2022]
Abstract
We study how the thermodynamic properties of the triangular plaquette model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in kinetically constrained models. As soon as we generalize the model to include additional interactions, a thermodynamic phase transition appears in the system. The additional interactions we consider are either short ranged, forming a regular lattice in the plane, or long ranged of the small-world kind. In the case of long-range interactions we call the new model the random-diluted TPM. We provide arguments that the model so modified should undergo a thermodynamic phase transition, and that in the long-range case this is a glass transition of the "random first-order" kind. Finally, we give support to our conjectures studying the finite-temperature phase diagram of the random-diluted TPM in the Bethe approximation. This corresponds to the exact calculation on the random regular graph, where free energy and configurational entropy can be computed by means of the cavity equations.
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Affiliation(s)
- Silvio Franz
- LPTMS, CNRS, Université Paris Sud et Université Paris-Saclay, 91405 Orsay, France
| | - Giacomo Gradenigo
- LPTMS, CNRS, Université Paris Sud et Université Paris-Saclay, 91405 Orsay, France.,IPhT, CEA Saclay, F-91191 Gif-sur-Yvette Cedex, France.,Université Grenoble Alpes, LIPHY, F-38000 Grenoble, France.,CNRS, LIPHY, F-38000 Grenoble, France
| | - Stefano Spigler
- LPTMS, CNRS, Université Paris Sud et Université Paris-Saclay, 91405 Orsay, France
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2
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Sasa SI. Pure glass in finite dimensions. PHYSICAL REVIEW LETTERS 2012; 109:165702. [PMID: 23215092 DOI: 10.1103/physrevlett.109.165702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2012] [Revised: 07/25/2012] [Indexed: 06/01/2023]
Abstract
Pure glass is defined as a thermodynamic phase in which typical equilibrium particle configurations have macroscopic overlaps with one of some special irregular configurations. By employing 128 types of artificial molecules, a pure glass model is constructed in the cubic lattice.
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Affiliation(s)
- Shin-ichi Sasa
- Department of Basic Science, The University of Tokyo, Tokyo 153-8902, Japan
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Hocky GM, Markland TE, Reichman DR. Growing point-to-set length scale correlates with growing relaxation times in model supercooled liquids. PHYSICAL REVIEW LETTERS 2012; 108:225506. [PMID: 23003622 DOI: 10.1103/physrevlett.108.225506] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2012] [Indexed: 06/01/2023]
Abstract
It has been demonstrated recently that supercooled liquids sharing simple structural features (e.g. pair distribution functions) may exhibit strikingly distinct dynamical behavior. Here we show that a more subtle structural feature correlates with relaxation times in three simulated systems that have nearly identical radial distribution functions but starkly different dynamical behavior. In particular, for the first time we determine the thermodynamic "point-to-set" length scale in several canonical model systems and demonstrate the quantitative connection between this length scale and the growth of relaxation times. Our results provide clues necessary for distinguishing competing theories of the glass transition.
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Affiliation(s)
- Glen M Hocky
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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Krzakala F, Zdeborová L. On melting dynamics and the glass transition. II. Glassy dynamics as a melting process. J Chem Phys 2011; 134:034513. [DOI: 10.1063/1.3506843] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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5
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Osenda O, Tamarit FA, Cannas SA. Nonequilibrium structures and slow dynamics in a two-dimensional spin system with competing long-range and short-range interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:021114. [PMID: 19792084 DOI: 10.1103/physreve.80.021114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2008] [Revised: 05/28/2009] [Indexed: 05/28/2023]
Abstract
We present a lattice spin model that mimics a system of interacting particles through a short-range repulsive potential and a long-range attractive power-law decaying potential. We perform a detailed analysis of the general equilibrium phase diagram of the model at finite temperature, showing that the only possible equilibrium phases are the ferromagnetic and the antiferromagnetic ones. We then study the nonequilibrium behavior of the model after a quench to subcritical temperatures, in the antiferromagnetic region of the phase diagram region, where the pair interaction potential behaves in the same qualitative way as in a Lennard-Jones gas. We find that even in the absence of quenched disorder or geometric frustration, the competition between interactions gives rise to nonequilibrium disordered structures at low enough temperatures that strongly slow down the relaxation of the system. This nonequilibrium state presents several features characteristic of glassy systems such as subaging, nontrivial fuctuation dissipation relations, and possible logarithmic growth of free-energy barriers to coarsening.
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Affiliation(s)
- Omar Osenda
- Instituto de Física de la Facultad de Matemática, Astronomía y Física (IFFAMAF-CONICET), Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Córdoba, Argentina.
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Chamon C. Quantum glassiness in strongly correlated clean systems: an example of topological overprotection. PHYSICAL REVIEW LETTERS 2005; 94:040402. [PMID: 15783534 DOI: 10.1103/physrevlett.94.040402] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2004] [Indexed: 05/24/2023]
Abstract
This Letter presents solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three-dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, (1) have no quenched disorder, (2) have solely local interactions, (3) have an exactly solvable spectrum, (4) have topologically ordered ground states, and (5) have slow dynamical relaxation rates akin to those of strong structural glasses.
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Affiliation(s)
- Claudio Chamon
- Physics Department, Boston University, Boston, Massachusetts 02215, USA
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Espriu D, Prats A. Dynamics of the two-dimensional gonihedric spin model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:046117. [PMID: 15600470 DOI: 10.1103/physreve.70.046117] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2004] [Revised: 06/02/2004] [Indexed: 05/24/2023]
Abstract
In this paper, we study dynamical aspects of the two-dimensional (2D) gonihedric spin model using both numerical and analytical methods. This spin model has vanishing microscopic surface tension and it actually describes an ensemble of loops living on a 2D surface. The self-avoidance of loops is parametrized by a parameter kappa . The kappa=0 model can be mapped to one of the six-vertex models discussed by Baxter, and it does not have critical behavior. We have found that allowing for kappa not equal 0 does not lead to critical behavior either. Finite-size effects are rather severe, and in order to understand these effects, a finite-volume calculation for non-self-avoiding loops is presented. This model, like his 3D counterpart, exhibits very slow dynamics, but a careful analysis of dynamical observables reveals nonglassy evolution (unlike its 3D counterpart). We find, also in this kappa=0 case, the law that governs the long-time, low-temperature evolution of the system, through a dual description in terms of defects. A power, rather than logarithmic, law for the approach to equilibrium has been found.
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Affiliation(s)
- D Espriu
- Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain.
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Crisanti A, Ritort F. Violation of the fluctuation–dissipation theorem in glassy systems: basic notions and the numerical evidence. ACTA ACUST UNITED AC 2003. [DOI: 10.1088/0305-4470/36/21/201] [Citation(s) in RCA: 291] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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9
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Dimopoulos P, Espriu D, Jané E, Prats A. Slow dynamics in the three-dimensional gonihedric model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:056112. [PMID: 12513561 DOI: 10.1103/physreve.66.056112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2002] [Revised: 06/27/2002] [Indexed: 05/24/2023]
Abstract
We study dynamical aspects of three-dimensional gonihedric spins by using Monte-Carlo methods. These models have a purely geometrical motivation, deriving from string and random surface theory. Here, however, we shall analyze this family of models just from a statistical point of view. In particular, we shall be concerned with their ability to exhibit remarkably slow dynamics and seemingly glassy behavior below a certain temperature T(g), without the need of introducing disorder of any kind. We consider first a Hamiltonian that takes into account only a four-spin term (kappa=0), where a first-order phase transition is well established. By studying the relaxation properties at low temperatures, we confirm that the model exhibits two distinct regimes. For T(g)<T<T(c), with long lived metastability and a supercooled phase, the approach to equilibrium is well described by a stretched exponential. For T<T(g), the dynamics appears to be logarithmic. We provide an accurate determination of T(g). We also determine the evolution of particularly long lived configurations. Next, we consider the case kappa=1, where the plaquette term is absent and the gonihedric action consists in a ferromagnetic Ising with fine-tuned next-to-nearest neighbor interactions. This model exhibits a second order phase transition. The consideration of the relaxation time for configurations in the cold phase reveals the presence of slow dynamics and glassy behavior for any T<T(c). Type-II aging features are exhibited by this model.
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Affiliation(s)
- P Dimopoulos
- Departament d'Estructura i Constituents de la Materia, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain.
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Crisanti A, Ritort F, Rocco A, Sellitto M. Inherent structures and nonequilibrium dynamics of one-dimensional constrained kinetic models: A comparison study. J Chem Phys 2000. [DOI: 10.1063/1.1324994] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Lipowski A, Johnston D. Cooling-rate effects in a model of glasses. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:6375-6382. [PMID: 11088314 DOI: 10.1103/physreve.61.6375] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/1999] [Indexed: 05/23/2023]
Abstract
Using Monte Carlo simulations we study cooling-rate effects in a three-dimensional Ising model with four-spin interactions. During coarsening, this model develops growing energy barriers, which at low temperature lead to very slow dynamics. We show that the characteristic zero-temperature length increases very slowly with the inverse cooling rate, similarly to the behavior of ordinary glasses. For computationally accessible cooling rates the model undergoes an ideal glassy transition, i.e., the glassy transition for a very small cooling rate coincides with a thermodynamic singularity. We also study the cooling of this model with a certain fraction of spins fixed. Due to such heterogeneous crystallization seeds, the final state strongly depends on the cooling rate. Only for a sufficiently fast cooling rate does the system end up in a glassy state, while slow cooling inevitably leads to a crystal phase.
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Affiliation(s)
- A Lipowski
- Department of Mathematics, Heriot-Watt University, EH14 4AS Edinburgh, United Kingdom and Department of Physics, A. Mickiewicz University, 61-614 Poznan, Poland
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Parisi G, Picco M, Ritort F. Continuous phase transition in a spin-glass model without time-reversal symmetry. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:58-68. [PMID: 11969737 DOI: 10.1103/physreve.60.58] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/1998] [Indexed: 04/18/2023]
Abstract
We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time-reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however, in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific-heat exponent. We expect the nature of the transition in this three-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.
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Affiliation(s)
- G Parisi
- Dipartimento di Fisica and INFN, Universita di Roma La Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy.
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Alegría A, Colmenero J, Mari PO, Campbell IA. Dielectric investigation of the temperature dependence of the nonexponentiality of the dynamics of polymer melts. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 59:6888-95. [PMID: 11969676 DOI: 10.1103/physreve.59.6888] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/1998] [Revised: 12/24/1998] [Indexed: 11/07/2022]
Abstract
Using broad band dielectric spectroscopy (10(-5)-10(9) Hz), combining time domain and frequency domain techniques, we study the temperature dependence of the non-Debye character of the alpha relaxation of polymer melts in the glass transition temperature T(g) range. The alpha relaxation process is described in terms of the Kohlrausch-Williams-Watts relaxation function which has a single parameter beta to characterize the nonexponentiality of the relaxation. At high temperatures, beta remains nearly insensitive to temperature changes, whereas in the vicinity of T(g) a nearly linear increasing of beta with temperature is found. The temperature range where the change of the beta(T) behavior occurs is located for all the polymers investigated around 1.2T(g). Moreover, our results indicate a common value of beta approximately equal to 1/3 at the temperature where the relaxation time diverges. The beta(T) behavior near T(g) is discussed in terms of a "rugged landscape" phase space which allows us to rationalize both the beta(T) behavior observed as well as the similarities of our findings near T(g) with the results reported in simulations on Ising spin glasses and other model systems.
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Affiliation(s)
- A Alegría
- Departamento de Física de Materiales y Centro Mixto CSIC-UPV/EHU, Facultad de Química, UPV/EHU, Apartado 1072, 20080 San Sebastián, Spain
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Stariolo DA, Arenzon JJ. Off-equilibrium dynamics of the frustrated Ising lattice gas. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 59:R4762-5. [PMID: 11969514 DOI: 10.1103/physreve.59.r4762] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/1998] [Indexed: 04/18/2023]
Abstract
We study by means of Monte Carlo simulations the off-equilibrium properties of a model glass, the frustrated Ising lattice gas in three dimensions. We have computed typical two times quantities, such as density-density autocorrelations and the autocorrelation of internal degrees of freedom. We find an aging scenario particularly interesting in the case of the density autocorrelations in real space that is very reminiscent of spin glass phenomenology. While this model captures the essential features of structural glass dynamics, its analogy with spin glasses may make possible its complete description using the tools developed in spin glass theory.
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Affiliation(s)
- D A Stariolo
- Departamento de Física, Universidade Federal de Viçosa, 36570-000 Viçosa MG, Brazil.
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Lipowski A. Glassy behaviour and semi-local invariance in Ising model with four-spin interaction. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/30/21/012] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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