Monte Carlo Study of Chiral Criticality –<i><i>X</i><i>Y</i></i>and Heisenberg Stacked-Triangular Antiferromagnets

TLDR

This study extends previous Monte Carlo simulations of XY and Heisenberg antiferromagnets on a 3‑D stacked‑triangular lattice, exploring their expected n = 2 and 3 chiral universality classes in light of recent renormalization‑group calculations and experiments. Simulations were performed on lattices of size L³ with 18 ≤ L ≤ 60, analyzing chiral ordering and determining chirality exponents. The simulations reveal continuous transitions with novel critical exponents (α = 0.34 ± 0.06, β = 0.253 ± 0.01, γ = 1.13 ± 0.05, ν = 0.54 ± 0.02 for XY; α = 0.24 ± 0.08, β = 0.30 ± 0.02, γ = 1.17 ± 0.07, ν = 0.59 ± 0.02 for Heisenberg) and specific‑heat amplitude ratios A⁺/A⁻ ≈ 0.36 ± 0.2 (XY) and 0.54 ± 0.2 (Heisenberg).

Abstract

The results of extensive Monte Carlo simulations are reported on X Y and Heisenberg antiferromagnets on a d =3-dimensional stacked-triangular lattice, which are expected to belong to the recently identified n =2 and 3 chiral universality classes, respectively. The lattices studied consist of L 3 spins with 18≤ L ≤60. The study is an extension of earlier Monte Carlo simulations for the same system with smaller lattices. A continuous transition characterized by the novel critical exponents is found with α=0.34±0.06, β=0.253±0.01, γ=1.13±0.05 and ν=0.54±0.02 for the X Y ( n =2) case, and with α=0.24±0.08, β=0.30±0.02, γ=1.17±0.07 and ν=0.59±0.02 for the Heisenberg ( n =3) case. The specific-heat amplitude ratio is estimated to be A + / A - =0.36±0.2 and A + / A - =0.54±0.2 in the n =2 and n =3 cases, respectively. The nature of the chiral ordering is also studied, and various chirality exponents are determined. The results are discussed in conjunction with the recent renormalization-group calculations and experiments.