Critical behaviour and scaling functions of the three-dimensional O(6) model

TL;DR

This study numerically analyzes the three-dimensional O(6) model to determine critical parameters, exponents, and scaling functions, confirming theoretical predictions and comparing with other O(N) models.

Contribution

It provides the first detailed numerical determination of critical coupling, exponents, and scaling functions for the 3D O(6) model, including effects of Goldstone modes.

Findings

Critical coupling J_c=1.42865(3)

Universal Binder cumulant g_r(J_c)=-1.94456(10)

Critical exponents: γ=1.604(6), β=0.425(2), ν=0.818(5)

Abstract

We numerically investigate the three-dimensional O(6) model on 12^3 to 120^3 lattices within the critical region at zero magnetic field, as well as at finite magnetic field on the critical isotherm and for several fixed couplings in the broken and the symmetric phase. We obtain from the Binder cumulant at vanishing magnetic field the critical coupling J_c=1.42865(3). The universal value of the Binder cumulant at this point is g_r(J_c)=-1.94456(10). At the critical coupling, the critical exponents \gamma=1.604(6), \beta=0.425(2) and \nu=0.818(5) are determined from a finite-size-scaling analysis. Furthermore, we verify predicted effects induced by massless Goldstone modes in the broken phase. The results are well described by the perturbative form of the model's equation of state. Our O(6)-result is compared to the corresponding Ising, O(2) and O(4) scaling functions. Finally, we study the finite-size-scaling behaviour of the magnetisation on the pseudocritical line.