A Variational Approach to Monte Carlo Renormalization Group

TL;DR

This paper introduces a variational Monte Carlo method for calculating renormalized couplings and critical exponents, effectively overcoming critical slowing down by using a bias potential to decorrelate coarse-grained variables, demonstrated on the 2D Ising model.

Contribution

It proposes a novel variational Monte Carlo approach for renormalization group calculations that reduces critical slowing down in statistical physics simulations.

Findings

Successfully computes critical exponents for the 2D Ising model.

Demonstrates improved efficiency over traditional Monte Carlo methods.

Provides a new framework for renormalization group analysis using variational principles.

Abstract

We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. The 2D Ising model is used to illustrate the method.