Hidden zero-temperature bicritical point in the two-dimensional anisotropic Heisenberg model: Monte Carlo simulations and proper finite-size scaling

TL;DR

This paper uses Monte Carlo simulations and finite-size scaling to demonstrate that the bicritical point in the two-dimensional anisotropic Heisenberg model occurs at zero temperature and is characterized by Heisenberg-like physics.

Contribution

The study connects Monte Carlo results with renormalization group theory, clarifying the nature and location of the bicritical point in the 2D anisotropic Heisenberg model.

Findings

Bicritical point occurs at T=0 in 2D.

Long length scale physics matches anisotropic nonlinear sigma model.

Monte Carlo data confirms Heisenberg-like bicritical behavior.

Abstract

By considering the appropriate finite-size effect, we explain the connection between Monte Carlo simulations of two-dimensional anisotropic Heisenberg antiferromagnet in a field and the early renormalization group calculation for the bicritical point in $2+\epsilon$ dimensions. We found that the long length scale physics of the Monte Carlo simulations is indeed captured by the anisotropic nonlinear $\sigma$ model. Our Monte Carlo data and analysis confirm that the bicritical point in two dimensions is Heisenberg-like and occurs at T=0, therefore the uncertainty in the phase diagram of this model is removed.