Restricted Boltzmann Machines for the Long Range Ising Models

TL;DR

This paper demonstrates how Restricted Boltzmann Machines can effectively model one-dimensional Long Range Ising models, achieving results comparable to established renormalization group methods through a novel training approach.

Contribution

The paper introduces a new method for training RBMs using Configuration with Probability to accurately reproduce Long Range Ising models.

Findings

RBMs successfully model LRI systems with high precision

RBM results align well with BDRG method

Proposed training improves RBM performance for physical models

Abstract

We set up Restricted Boltzmann Machines (RBM) to reproduce the Long Range Ising (LRI) models of the Ohmic type in one dimension. The RBM parameters are tuned by using the standard machine learning procedure with an additional method of Configuration with Probability (CwP). The quality of resultant RBM are evaluated through the susceptibility with respect to the magnetic external field. We compare the results with those by Block Decimation Renormalization Group (BDRG) method, and our RBM clear the test with satisfactory precision.