Corrections to finite--size scaling in the phi^4 model on square lattices

TL;DR

This study investigates correction-to-scaling phenomena in the 2D phi^4 model, revealing multiple correction exponents and demonstrating differences from the 2D Ising model through analytical and Monte Carlo analyses.

Contribution

The paper provides non-perturbative analytical insights and extensive Monte Carlo data showing the presence of multiple correction exponents in the 2D phi^4 model, highlighting deviations from Ising model corrections.

Findings

Corrections with exponents 3/4, 1/2, and ~1/4 are identified.

Corrections with omega_l < 1 diminish near the Ising limit.

The correction structure differs from the 2D Ising model.

Abstract

Corrections to scaling in the two-dimensional scalar phi^4 model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L (from 4 to 1536) and different values of the phi^4 coupling constant lambda, i.~e., lambda = 0.1, 1, 10. According to our analysis, amplitudes of the nontrivial correction terms with the correction-to-scaling exponents omega_l < 1 become small when approaching the Ising limit (lambda --> infinity), but such corrections generally exist in the 2D phi^4 model. Analytical arguments show the existence of corrections with the exponent 3/4. The numerical analysis suggests that there exist also corrections with the exponent 1/2 and, very likely, also corrections with the exponent about 1/4, which are detectable at lambda = 0.1. The numerical tests clearly show that the structure of corrections to scaling in the 2D phi^4 model differs from the usually expected one in the 2D Ising model.