The three-dimensional Ising spin glass in an external magnetic field: the role of the silent majority

Abstract

Abstract. We perform equilibrium parallel-tempering simulations of the 3D Ising Edwards-Anderson spin glass in a field, using the Janus computer. A traditional analysis shows no signs of a phase transition. Yet, we encounter dramatic fluctuations in the behaviour of the model: Averages over all the data only describe the behaviour of a small fraction of it. Therefore we develop a new approach to study the equilibrium behaviour of the system, by classifying the measurements as a function of a conditioning variate. We propose a finite-size scaling analysis based on the probability distribution function of the conditioning variate, which may accelerate the convergence to the thermodynamic limit. In this way, we find a non-trivial spectrum of behaviours, where a part of the measurements behaves as the average, while the majority of them shows signs of scale invariance. As a result, we can estimate the temperature interval where the phase transition in a field ought to lie, if it exists. Although this would-be critical regime is unreachable with present resources, the numerical challenge is finally well posed.

Numerical detection of the Gardner transition in a mean-field glass former

“…The development of an exponential tail at the critical point has been observed and studied for spin glasses in a field [59,60]. The effect is thought to be due to disorder.…”

Spin Glasses

“…The discussion will focus entirely on the analysis of the data and on the results. We want to stress, in this context, that the equilibrium MC simulations performed in [BJ14a] required huge numerical efforts. On the one hand, lower temperatures drastically increased thermalization times; on the other hand, the significance of the results depends upon the size of the systems we are able to simulate.…”

“…It would not have been possible to attain the results published in [BJ14a] with the mere use of ordinary computational resources. We drew upon (HPC) on one side by making use of the Janus dedicated computer to simulate the largest lattices, and on the other by simulating the smaller systems on a large CPU cluster, Memento.…”

“…We will instead focus on the result of equilibrium simulations performed on Janus, using lattices up to L = 32 [BJ14a]. 3 For further reference we…”

From local to global ground states in Ising spin glasses

“…On the other hand, for three dimensions and higher, there is believed to be a phase transition temperature T c > 0 with a domain wall exponent θ > 0 for excitations above the ground state 13 . Similarly, we can consider random models with nonzero fields [14][15][16] and denote standard deviation of the field magnitude by h . In this case, we consider the quantity…”