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arXiv · 1709.01715

$XY$ model with higher-order exchange

Milan Žukovič·Georgii Kalagov
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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 $η= T/[2 πJ(p,α)]$, nonlinearly dependent on the parameters $p$ and $α$ 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.

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Milan Žukovič, Georgii Kalagov. 2017-09-06. $XY$ model with higher-order exchange. https://doi.org/10.1103/physreve.96.022158

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