Finite size effects on measures of critical exponents in d=3 O(N) models

TL;DR

This paper investigates the critical exponents of 3D O(N) models for N=2,3,4, revealing finite size effects and providing extrapolated values that align with epsilon-expansion predictions rather than previous Monte Carlo results.

Contribution

It introduces a new method for extrapolating critical exponents in 3D O(N) models accounting for finite size effects, challenging prior Monte Carlo findings.

Findings

Extrapolated eta exponents agree with epsilon-expansions.

Measured tensorial magnetization and nu exponents.

Identified finite size effects impacting critical exponent estimates.

Abstract

We study the critical properties of three-dimensional O(N) models, for N=2,3,4. Parameterizing the leading corrections-to-scaling for the $\eta$ exponent, we obtain a reliable infinite volume extrapolation, incompatible with previous Monte Carlo values, but in agreement with $\epsilon$-expansions. We also measure the critical exponent related with the tensorial magnetization as well as the $\nu$ exponents and critical couplings.