arXiv:cond-mat/9703253 · Journal of Physics A Mathematical and General

Four-dimensional spin glasses in a magnetic field have a mean-field-like phase

Enzo Marinari, Giorgio Parisi A, F Zuliani

Published Jan 30, 1998• 22 citations

Abstract

By using numerical simulations we show that the four-dimensional Edwards Anderson spin glass in magnetic field undergoes a mean-field-like phase transition. We use a dynamical approach: we simulate large lattices (of volume V ) and work out the behaviour of the system in a limit where both t and V go to infinity, but where the limit is taken first. By showing that the dynamic overlap q converges to a value smaller than the static one we exhibit replica symmetry breaking. The critical exponents are compatible with those obtained by mean-field computations.

DOI: 10.1088/0305-4470/31/4/008

Related papers

Numerical simulations of the four-dimensional Edwards-Anderson spin glass with binary couplings

Enzo Marinari, Francesco Zuliani

We present numerical results that allow a precise determination of the transition point and of the critical exponents of the four-dimensional Edwards-Anderson spin glass with binary quenched random couplings. We show that the low-temperature phase undergoes replica symmetry breaking. We obtain results on large lattices, up to a volume V = 10 4 : we use finite-size scaling to show the relevance of our results in the infinite volume limit.

arXiv:cond-mat/9904303Journal of Physics A Mathematical and GeneralOct 13, 199936 citations

Critical behaviour of the four-dimensional spin glass in magnetic field

Enzo Marinari, C. Naitza, Francesco Zuliani

We present numerical simulations of the four-dimensional Edwards Anderson Ising spin glass with binary couplings. Our results, in the midst of strong finite-size effects, suggest the existence of a spin-glass phase transition. We present a preliminar determination of critical exponents. We discuss spin-glass susceptibilities, cumulants of the overlap and energy overlap probability distributions, finite-size effects, and the behaviour of the disorder-dependent and integrated probability distributions.

arXiv:cond-mat/9802224Journal of Physics A Mathematical and GeneralJul 31, 199825 citations

Phase structure of the three-dimensional Edwards-Anderson spin glass

Enzo Marinari, Giorgio Parisi A, Juan Jesus Ruiz-Lorenzo

We characterize numerically the properties of the phase transition of the three-dimensional Ising spin glass with Gaussian couplings and of the low-temperature phase. We compute critical exponents on large lattices. We study in detail the overlap probability distribution and the equilibrium overlap-overlap correlation functions. We find a clear agreement with off-equilibrium results from previous work. These results strongly support the existence of a continuous spontaneous replica symmetry breaking in three-dimensional spin glasses.

arXiv:cond-mat/9802211Physical review. B, Condensed matterDec 1, 1998108 citations

Mean field dynamical exponents in finite-dimensional Ising spin glass

Giorgio Parisi A, Paola Ranieri, Federico Ricci‐Tersenghi +1 more

We have studied numerically the remanent magnetization in the six- and eight-dimensional Ising spin glass and we have compared it with the behaviour observed in the SK model, that we have also computed analytically. We also report the value of the dynamical critical exponent z in six dimensions measured in three different ways: from the behaviour of the energy and the susceptibility as a function of the Monte Carlo time and by studying the overlap - overlap correlation function as a function of space and time. These three results are in very good agreement with the mean field prediction z = 4. Finally we have checked numerically the analytical prediction, obtained by assuming spontaneously broken replica symmetry, for the most singular part of the propagator in the spin-glass phase. This last result supports the existence of spontaneously broken replica symmetry in finite-dimensional spin glasses.

arXiv:cond-mat/9702030Journal of Physics A Mathematical and GeneralOct 21, 199726 citations

The connection between statics and dynamics of spin glasses

Matthew Wittmann, A. P. Young

Abstract We present results of numerical simulations on a one-dimensional Ising spin glass with long-range interactions. Parameters of the model are chosen such that it is a proxy for a short-range spin glass above the upper critical dimension (i.e. in the mean-field regime). The system is quenched to a temperature well below the transition temperature and the growth of correlations is observed. The spatial decay of the correlations at distances less than the dynamic correlation length agrees quantitatively with the predictions of a static theory, the ‘metastate’, evaluated according to the replica symmetry breaking (RSB) theory. We also compute the dynamic exponent z ( T ) defined by and find that it is compatible with the mean-field value of the critical dynamical exponent for short range spin glasses.

arXiv:1504.07709Journal of Statistical Mechanics Theory and ExperimentJan 1, 20168 citations

Replica symmetry breaking in four-dimensional spin glasses

Giorgio Parisi A, Félix Ritort

In this paper we present a new numerical method to test mean-field ideas in the Ising spin glass at finite dimensions. Very large sizes can be studied and numerical results are presented in the case of the four-dimensional Ising spin glass. New exponents are introduced within the spin-glass phase and we find evidence of a phase with replica broken features.

Journal of Physics A Mathematical and GeneralDec 7, 199318 citations