Universal behavior in the static and dynamic properties of the $α$-XY model

Andrea Giansanti; Daniele Moroni; Alessandro Campa

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Universal behavior in the static and dynamic properties of the $α$-XY model

Andrea Giansanti·Daniele Moroni·Alessandro Campa

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Abstract

The $α$-XY model generalizes, through the introduction of a power-law decaying potential, a well studied mean-field hamiltonian model with attractive long-range interactions. In the $α$-model, the interaction between classical rotators on a lattice is gauged by the exponent $α$ in the couplings decaying as $r^α$, where $r$ are distances between sites. We review and comment here a few recent results on the static and dynamic properties of the $α$-model. We discuss the appropriate $α$ dependent rescalings that map the canonical thermodynamics of the $α$-model into that of the mean field model. We also show that the chaotic properties of the model, studied as a function of $α$ display an universal behaviour.

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Andrea Giansanti, Daniele Moroni, Alessandro Campa. 2000-11-08. Universal behavior in the static and dynamic properties of the $α$-XY model. https://arxiv.org/abs/cond-mat/0007422

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