Reducing finite-size effects with reweighted renormalization group transformations

TL;DR

This paper introduces a combined histogram reweighting and two-lattice matching Monte Carlo renormalization group method to efficiently compute critical exponents and reduce finite-size effects in lattice systems, including complex actions.

Contribution

It presents a novel approach that integrates reweighting with RG transformations to improve accuracy and efficiency in finite lattice simulations.

Findings

Successfully determined critical exponents for 2D φ^4 theory.

Quantified computational efficiency gains over traditional methods.

Extended applicability to systems with complex-valued actions.

Abstract

We combine histogram reweighting techniques with the two-lattice matching Monte Carlo renormalization group method to conduct computationally efficient calculations of critical exponents on systems with moderately small lattice sizes. The approach, which relies on the construction of renormalization group mappings between two systems of identical lattice size to partially eliminate finite-size effects, and the use of histogram reweighting to obtain computationally efficient results in extended regions of parameter space, is utilized to explicitly determine the renormalized coupling parameters of the two-dimensional $\phi^{4}$ scalar field theory and to extract multiple critical exponents. We conclude by quantifying the computational benefits of the approach and discuss how reweighting opens up the opportunity to extend Monte Carlo renormalization group methods to systems with complex-valued actions.