Order-parameter fluctuations (OPF) in spin glasses: Monte Carlo simulations and exact results for small sizes

Abstract

The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in 2 which show that two of these parameters, G and Gc, take universal values in the limT →0. In this paper we present a detailed study of parameters measuring OPF for two meanfield models with and without time-reversal symmetry which exhibit different patterns of replica symmetry breaking below the transition: the Sherrington-Kirkpatrick model with and without a field and the Ising p-spin glass (p=3). We give numerical results and analyze the consequences which replica equivalence imposes on these models in the infinite volume. We give evidence for the transition in each system and discuss the character of finite-size effects. Furthermore, a comparative study between this new family of parameters and the usual Binder cumulant analysis shows what kind of new information can be extracted from the finite T behavior of these quantities. The two main outcomes of this work are: 1) Parameters measuring OPF give better estimates than the Binder cumulant for Tc and even for very small systems they give evidence for the transition. 2) For systems with no time-reversal symmetry, parameters defined in terms of connected quantities are the proper ones to look at.

Squared interaction matrix Sherrington-Kirkpatrick model for a spin glass

“…5 we show the kurtosis parameter B as a function of T for different sizes. In the same way as in the SK model 21 we find a crossing at a temperature close to T c ϭ2. This crossing turns out to be also present for the OPF parameter G as shown in Fig.…”

“…This last parameter is the most successful example of what are referred to as orderparameter fluctuation parameters ͑OPF parameters͒. 21 Before showing the results let us mention that, while for the positive-K model we achieved thermalization in a range of temperatures in the vicinity of T c , for the negative-K model thermalization was hardly achieved due to the quite small acceptance rate for all the temperatures simulated. This behavior is due to the small value of the relevant temperatures of the KϽ0 model where the transition occurs ͑one order of magnitude smaller͒.…”

Predictive power of MCT: numerical testing and finite size scaling for a mean field spin glass

“…In figure 5, we plot the usual Binder parameter, For generic 1-RSB transitions, Picco et al [49] have argued that these two coefficients are zero for T > T s (in the thermodynamic limit), non zero for T < T s − s . The fact that the Binder coefficient is negative when T → T − s is simply related to the appearance of a peak in P (q) for q = 0.…”

“…Following [49], we plot in figure (5) the coefficient A(T ) defined as: that signals [50] the onset of the non self-averaging behavior of q 2 . In figure 5, we plot the usual Binder parameter, For generic 1-RSB transitions, Picco et al [49] have argued that these two coefficients are zero for T > T s (in the thermodynamic limit), non zero for T < T s − s .…”

Monte Carlo study of the ordering of the weakly anisotropic Heisenberg spin glass in magnetic fields

“…Such a system was theoretically analyzed in Ref. 41 , where the behavior of the Binder ratio g ′ χ in the thermodynamic limit was reported as shown in Fig.6.…”