Critical behaviour and Scaling functions for the three-dimensional O(6) spin model with external field

TL;DR

This study numerically analyzes the three-dimensional O(6) spin model, determining critical parameters, exponents, and scaling functions, and compares the equation of state with other O(N) models.

Contribution

It provides precise numerical estimates of critical coupling, exponents, and scaling functions for the 3D O(6) model, extending understanding of its critical behavior.

Findings

Critical coupling J_c=1.42865(5)

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

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

Abstract

We numerically investigate the three-dimensional O(6) model on 12^3 to 120^3 lattices. From Binder's cumulant at vanishing magnetic field we obtain the critical coupling J_c=1.42865(5) and verify this value with the \chi^2-method. The universal value of Binder's cumulant at this point is g_r(J_c)=-1.94456(10). At the critical coupling we find the critical exponents \nu=0.818(5), \beta=0.425(2) and \gamma=1.604(6) from a finite size scaling analysis. We also determine the finite-size-scaling function on the critical line and the equation of state. Our O(6)-result for the equation of state is compared to the Ising, O(2) and O(4) results.