Monte Carlo simulation of the three-dimensional XY model with bilinear-biquadratic exchange interaction

TL;DR

This study uses Monte Carlo simulations to explore the phase diagram of the 3D XY model with bilinear and biquadratic interactions, revealing complex phase transitions and critical behavior similar to the standard XY model.

Contribution

It provides the first detailed phase diagram and critical analysis of the 3D XY model with bilinear-biquadratic exchange interactions, identifying multiple ordered phases and transition types.

Findings

Identified a single second-order phase transition at high J/J' ratios.

Discovered two separate transitions at J/J'<0.35, including quadrupole and dipole-quadrupole orderings.

Critical exponents are close to those of the conventional XY model.

Abstract

The three-dimensional XY model with bilinear-biquadratic exchange interactions $J$ and $J'$, respectively, has been studied by Monte Carlo simulations. From the detailed analysis of the thermal variation of various physical quantities, as well as the order parameter and energy histogram analysis, the phase diagram including two different ordered phases has been determined. There is a single phase boundary from a paramagnetic to a dipole-quadrupole ordered phase, which is of second order in a high $J/J'$ ratio region, changing to a first-order one for $0.35 \leq J/J' \leq 0.5$. Below $J/J'=0.35$ there are two separate transitions: the first one to the quadrupole long-range order (QLRO) phase at higher temperatures, followed by another one to the dipole-quadrupole long-range order (DLRO) phase at lower temperatures. The finite-size scaling analysis yields values of the critical exponents for both the DLRO and QLRO transitions close to the values for the conventional XY model which includes no biquadratic exchange.