Lee-Yang Zeroes and Logarithmic Corrections in the $\Phi^4_4$ Theory

TL;DR

This paper investigates the logarithmic corrections to mean-field critical behaviour in the four-dimensional $\

Contribution

It provides an analytical and numerical analysis of logarithmic corrections in $\

Findings

Finite-size scaling theory for Lee-Yang and temperature zeroes with logarithmic corrections

Monte Carlo simulations on lattices up to $24^4$ confirm analytical predictions

Logarithmic corrections agree well with theoretical expectations

Abstract

The leading mean-field critical behaviour of $\phi^4_4$-theory is modified by multiplicative logarithmic corrections. We analyse these corrections both analytically and numerically. In particular we present a finite-size scaling theory for the Lee-Yang zeroes and temperature zeroes, both of which exhibit logarithmic corrections. On lattices from size $8^4$ to $24^4$, Monte-Carlo cluster methods and multi-histogram techniques are used to determine the partition function zeroes closest to the critical point. Finite-size scaling behaviour is verified and the logarithmic corrections are found to be in good agreement with our analytical predictions.