Analysis of Ising model using neural networks

Abstract

This work attempts to study the simplest classical model systems that describe the physics of phase transitions- nearest neighbour Ising models using neural networks which are often associated with artificial intelligence. There are two distinct parts to this- one, extracting useful physical information like order parameters from thermalized samples and two, finding more efficient ways of obtaining the thermalized samples in the first place. Existing works already show that feeding thermalized samples to a trained neural network to identify any points in the phase space (like temperature) associated with drastic changes like phase transition without identifying order parameters. We note that the outputs of these networks in the phase space describe a certain order parameter that's similar yet different from a standard order parameter like magnetization. We study the sensitivity of neural networks to changes along the phase space of Edwards Anderson (EA) model with a stochastic Hamiltonian. Traditionally, Markov Chain Monte Carlo (MCMC) methods are used to sample the thermalised spin lattices like Ising. A recent work proposed an alternative- using autoregressive neural neural networks that produces unchained, uncorrelated samples of thermalized spin lattices along with log-probabilities for every sample. However, their network was computationally expensive to implement on large lattices. We build on this to optimize the network design for speed by using insights from the underlying Boltzmann distribution for Ising models. We then obtain a method that can sample lattices with time complexity atmost linear to the number of spins in the lattice, making it a truly viable alternative to MCMC as a sampling procedure.