Tricritical transition in the classical XY model on Kagom\'e lattice under local anisotropy

TL;DR

This study investigates the phase transition behavior of the classical XY model on a Kagomé lattice with anisotropy, revealing a tricritical point where the transition changes from first to second order and suggesting a new universality class.

Contribution

It combines mean-field and Monte Carlo methods to identify a tricritical point and analyze universality classes in the XY model on Kagomé lattice with anisotropy.

Findings

First-order transition at low anisotropy

Second-order transition at high anisotropy

Evidence of a new tricritical universality class

Abstract

Using mean-field theory and high resolution Monte Carlo simulation technique based on multi-histogram method, we have investigated the critical properties of an antiferromagnetic XY model on the 2D Kagom\'e lattice, with single ion easy-axes anisotropy. The mean-field theory predicts second-order phase transition from disordered to all-in all-out state for any value of anisotropy for this model. However, Monte Carlo simulations result in first order transition for small values of anisotropy which turns to second order with increasing strength of anisotropy, indicating the existence of a tricritical point for this model. The critical exponents, obtained by finite-size scaling methods, show that the transition is in Ising universality class for large values of anisotropy, while the critical behaviour of the system deviates from 2D-$\phi^6$ model near the tricritical point. This suggests the possibility for existence of a new tricritical universality in two-dimensions.