Canonical Demon Monte Carlo Renormalization Group

TL;DR

This paper introduces a novel Monte Carlo renormalization group method using canonical demons to accurately compute renormalized couplings across various models, demonstrated on the $O(3)$ nonlinear sigma model.

Contribution

The paper presents a new demon-based Monte Carlo RG technique that avoids systematic errors of previous methods, applicable to lattice spin and gauge models.

Findings

Successfully computed renormalized couplings for the $O(3)$ model.

Method eliminates systematic errors from ensemble mismatches.

Applicable to a broad class of lattice models.

Abstract

We describe a new method to compute renormalized coupling constants in a Monte Carlo renormalization group calculation. The method can be used for a general class of models, e.g., lattice spin or gauge models. The basic idea is to simulate a joint system of block spins and canonical demons. In contrast to the Microcanonical Renormalization Group invented by Creutz et al. our method does not suffer from systematical errors stemming from a simultaneous use of two different ensembles. We present numerical results for the $O(3)$ nonlinear $\sigma$-model.