Crossover Behavior from Decoupled Criticality

TL;DR

This study investigates the phase transition behavior of a two-sublattice XY spin model with biquadratic coupling, revealing a crossover from a continuous to a first-order transition through Monte Carlo simulations.

Contribution

It provides evidence that the phase transition in this model is ultimately first-order, challenging the expectation of a continuous transition at the 3D-XY fixed point.

Findings

Flow towards a first-order transition without a new fixed point

No separatrix observed in the crossover behavior

Supports the conclusion of a first-order transition asymptotically

Abstract

We study the thermodynamic phase transition of a spin Hamiltonian comprising two 3D magnetic sublattices. Each sublattice contains XY spins coupled by the usual bilinear exchange, while spins in different sublattices only interact via biquadratic exchange. This Hamiltonian is an effective model for XY magnets on certain frustrated lattices such as body centered tetragonal. By performing a cluster Monte Carlo simulation, we investigate the crossover from the 3D-XY fixed point (decoupled sublattices) and find a systematic flow toward a first-order transition without a separatrix or a new fixed point. This strongly suggests that the correct asymptotic behavior is a first-order transition.