Dynamic critical behavior in Ising spin glasses

Abstract

The critical dynamics of Ising spin glasses with Bimodal, Gaussian, and Laplacian interaction distributions are studied numerically in dimensions 3 and 4. The data demonstrate that in both dimensions the critical dynamic exponent zc, the non-equilibrium autocorrelation decay exponent λc/zc, and the critical fluctuation-dissipation ratio X∞ all vary strongly and systematically with the form of the interaction distribution.

Critical behavior of three-dimensional Ising spin glass models

“…to belong to a universality class which is independent of the details of the model and, in particular, of the disorder distribution. Several numerical works 5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33 have addressed these issues, considering various Ising spin-glass models, characterized by different disorder distributions, with or without dilution. Over the years many estimates of the critical exponents have been obtained.…”

Universality and universal finite-size scaling functions in four-dimensional Ising spin glasses

“…The conclusion that universality holds has also been obtained via other methods such as high-temperature series expansions 5 where the critical exponent γ has been studied. Studies of dynamical quantities however have yielded different critical exponents for different disorder distributions, 6,7,8,9 although it is unclear up to what level it can be expected that "dynamical universality" can be compared to universality in thermal equilibrium.…”

Out-of-equilibrium finite-size method for critical behavior analyses

“…Instead, it is larger than those of Refs. [5,6,12]. However, note that in all these works no scaling corrections, crucial to control possible systematic errors, were included in the analyses.…”

“…The method we discuss is somewhat different from previous off-equilibrium methods (see, e.g., Refs. [4][5][6][7][8][9][10][11][12] and references therein). Indeed, in most of those works it is generally assumed that L is so large that finite-size effects are negligible, a condition that is easily satisfied in pure systems but not in the disordered case.…”