First-order transition in $XY$ model with higher-order interactions

TL;DR

This study investigates how adding higher-order interactions to the XY model affects its phase transition, revealing a shift from continuous to first-order transition as more terms are included, supported by Monte Carlo simulations.

Contribution

It demonstrates that higher-order interactions can fundamentally change the nature of phase transitions in the XY model, providing new insights into critical phenomena.

Findings

Higher-order interactions modify the potential shape.

Transition changes from continuous to first order beyond a certain number of terms.

Finite-size scaling and energy histograms support the first-order transition.

Abstract

The effect of inclusion of higher-order interactions in the {\it XY} model on critical properties is studied by Monte Carlo simulations. It is found that an increasing number of the higher-order terms in the Hamiltonian modifies the shape of the potential, which beyond a certain value leads to the change of the nature of the transition from continuous to first order. The evidence for the first-order transition is provided in the form of the finite-size scaling and the energy histogram analysis. A rough phase diagram is presented as a function of the number of the higher-order interaction terms.