Investigation of the spin glass density of states using a combination of Monte Carlo method and neural network

Abstract

The study of magnetic systems, spin glasses, and their states, is an actively developed field of statistical physics. Spin glass models are studied in various scientific contexts, including experimental physics, condensed matter physics, theoretical physics, mathematical statistical physics and, more recently, probability theory [1 - 3]. The problem of finding the ground states (GS), i.e. states with the lowest energy is a very difficult task due to the macroscopic degeneracy and frustrations that are exist in various realistic spin glass models. In fact, it’s well known that finding the GS, of a spin glass in a three-dimensional lattice is an NP-complete problem, which means that this challenge is at least as difficult as the hardest problems of practical interest. The system of interest is the Edwards-Anderson (EA) spin glass model [4] in two-dimensional (2D) lattice, with bimodal distribution of bonds. In present work, for simulation we used a combination of our Hybrid Multispin Method (HMM) [5] and Long Short-Term Memory (LSTM) - an artificial recurrent neural network (RNN) architecture [6] with Boltzmann distribution. HMM’s advantages are the ability to increase the number of simultaneously gathered statistical-thermodynamic parameters without noticeable speed and efficiency loss, and the ability to search for configurations of the ground and low-energy states. The usage of machine learning in statistical physics began relatively recently but is developing rapidly. Neural networks have become popular tool due to the high speed of their training and accuracy of predictions. LSTM with Boltzmann distribution is useful for certain types of prediction that require the network to retain information for longer periods of time that traditional RNNs encounter. In our research, MC algorithm generated a training data set which is configurations of SG system. The trained predicted system configurations, which are using for the next computing cycle for HMM. Such iterative approach allows us to efficiently simulate the spin-glass systems even in the low-temperature regime, avoiding the critical slowing down that plague of usual MC simulation. This work was supported by the state task of the MSHE of Russia No. 0657-2020-0005.