Critical Behavior of the Antiferromagnetic Heisenberg Model on a Stacked Triangular Lattice

TL;DR

This paper uses large-scale Monte Carlo simulations to estimate critical exponents of the antiferromagnetic Heisenberg model on a stacked triangular lattice, revealing unexpected complexity in its critical behavior.

Contribution

It provides new estimates of critical exponents that challenge existing perturbative Renormalization Group predictions and suggest a richer RG flow structure.

Findings

Critical exponents estimated: γ/ν=2.011±0.014, ν=0.585±0.009

Results contradict 2+ε RG calculations, aligning more with 4−ε Landau-Ginzburg analysis

Indicates complex RG flow structure depending on dimensionality and order parameter components

Abstract

We estimate, using a large-scale Monte Carlo simulation, the critical exponents of the antiferromagnetic Heisenberg model on a stacked triangular lattice. We obtain the following estimates: $\gamma/\nu= 2.011 \pm .014 $, $\nu= .585 \pm .009 $. These results contradict a perturbative $2+\epsilon$ Renormalization Group calculation that points to Wilson-Fisher O(4) behaviour. While these results may be coherent with $4-\epsilon$ results from Landau-Ginzburg analysis, they show the existence of an unexpectedly rich structure of the Renormalization Group flow as a function of the dimensionality and the number of components of the order parameter.