$XY$ model with higher-order exchange

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.

arXiv comment17 pages, 7 figures

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• Phase diagrams of antiferromagnetic $XY$ model on a triangular lattice with higher-order interactions
• Monte Carlo study of the phase transitions in the classical XY ferromagnets with random anisotropy
• ${\mathbb{Z}}_n$ modified XY and Goldstone models and vortex confinement transition
• Phases of active matter in two dimensions
• Phase transitions in the anisotropic XY ferromagnet with quenched nonmagnetic impurity
• XY model with competing higher-order interactions
• Phase behavior of hard circular arcs
• Generalized $XY$ model with competing antiferromagnetic and antinematic interactions