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.
