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Abstract

We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss what happens in finite-dimensional, realistic spin glasses. Together with a detailed review of some of the most important features, facts, data, and phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correlation functions, interfaces, overlaps, pure states, random field, and the dynamical approach. We present new numerical results for the behaviors of coupled replicas and about the numerical verification of sum rules, and we review some of the available numerical results that we consider of larger importance (for example, the determination of the phase transition point, the correlation functions, the window overlaps, and the dynamical behavior of the system).

Generalized off-equilibrium fluctuation-dissipation relations in random Ising systems

“…The only prediction which seems to be compatible with our data is the one coming from the mean-field-like scenario of finite-dimensional spin glasses [8,26,27], which predicts a full replica symmetry breaking solution for the EdwardsAnderson model and assign it to category C. In Fig. 7 we also plot a second straight line to emphasize the curvature of the data in the aging regime.…”

The ± J spin glass in Migdal-Kadanoff approximation

“…While the scaling arguments by Krzakala and Martin [10] predict a decrease of P (q = 0, L) at zero temperature at least with an exponent −d s /2 (if one assumes with them that the system shows RSB, implying θ = 0), which lies somewhere between -1.1 and -1.3, the best Monte-Carlo simulations find only a value around -0.9 [11,14]. Other Monte-Carlo simulations giving a considerably smaller exponent probably do not sample the ground state configurations with the appropriate weights (see the comment by Marinari et al [15] on the simulations by Hatano and Gubernatis [16], and the remarks by Palassini and Young [11] on the simulations by Hartmann [17].) Our findings of a surprisingly slow approach to the correct asymptotic scaling can reconcile the Monte-Carlo results with the predictions by Krzakala and Martin, and also with our predictions based on the droplet picture (where the asymptotic exponent is around -1.4 or -1.5), which we believe to be the correct description of the spin-glass phase.…”

“…While many Monte-Carlo simulations show properties conforming to the replica-symmetry-breaking (RSB) scenario (implying many low-temperature states and a lack of self-averaging) [1,2], other simulations [3] and analytical arguments [4] favour the droplet picture (a scaling theory based on the existence of only one lowtemperature state and its time reverse). The ambiguities stem from the difficulty in reaching the asymptotic limit of low temperatures and large system sizes.…”

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

“…In figure 1, we display results for very small sizes (N = 4 − 11) obtained from exact computations of the partition function (such analysis was done in 23 for the SK model) averaging over 10000 samples of Gaussian quenched couplings with variance 1/N . In figure 2 we show results for larger sizes (N = 32, 64, 128, 256, 512) using the parallel tempering technique 24,25 with binary couplings. The number of samples ranges from 1000 for the smallest size, N = 32, to 250 for the biggest one, N = 512.…”