Renormalization Group Analysis of Finite-Size Scaling in the $\Phi^4_4$ Model

TL;DR

This paper develops a finite-size scaling theory for the $^4_4$ model using renormalization group techniques, highlighting logarithmic corrections and validating predictions through Monte Carlo simulations.

Contribution

It introduces a non-perturbative finite-size scaling framework for the $^4_4$ model, emphasizing the role of partition function zeroes and logarithmic corrections.

Findings

Good quantitative agreement between Monte Carlo results and analytical predictions.

Leading scaling behavior matches mean field theory.

Logarithmic corrections are significant in finite-size scaling.

Abstract

A finite-size scaling theory for the $\phi^4_4$ model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the leading scaling behaviour is identical to that of mean field theory, there exist multiplicative logarithmic corrections too. A non-perturbative test of these formulae in the form of a high precision Monte Carlo analysis reveals good quantitative agreement with the analytical predictions.