$XY$ model with higher-order exchange

TL;DR

This paper investigates an extended XY model with infinite higher-order interactions, revealing a low-temperature quasi-long-range order and a temperature-driven crossover from BKT to first-order transitions influenced by topological excitations.

Contribution

It introduces a generalized XY model with infinite higher-order terms and analyzes its phase transitions and topological excitations using spin-wave theory and Monte Carlo simulations.

Findings

Identifies a quasi-long-range order phase with algebraic decay of correlations.

Discovers a crossover from BKT to first-order transition depending on model parameters.

Highlights the influence of topological vortices on the transition nature.

Abstract

An $XY$ model, generalized by inclusion of up to an infinite number of higher-order pairwise interactions with an exponentially decreasing strength, is studied by spin-wave theory and Monte Carlo simulations. At low temperatures the model displays a quasi-long-range order phase characterized by an algebraically decaying correlation function with the exponent $\eta = T/[2 \pi J(p,\alpha)]$, nonlinearly dependent on the parameters $p$ and $\alpha$ that control the number of the higher-order terms and and the decay rate of their intensity, respectively. At higher temperatures the system shows a crossover from the continuous Berezinskii-Kosterlitz-Thouless to the first-order transition for the parameter values corresponding to a highly nonlinear shape of the potential well. The role of of topological excitations (vortices) in changing the nature of the transition is discussed.