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

• Main Authors: Giansanti, Andrea, Moroni, Daniele, Campa, Alessandro
• Format: Journal Article
• Language: English
• Published: 26-07-2000
• Subjects: Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.cond-mat/0007422

Chaos, Solitons and Fractals 13, 407 (2002) The $\alpha$-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 $\alpha$-model, the interaction between
classical rotators on a lattice is gauged by the exponent $\alpha$ in the
couplings decaying as $r^\alpha$, where $r$ are distances between sites. We
review and comment here a few recent results on the static and dynamic
properties of the $\alpha$-model. We discuss the appropriate $\alpha$ dependent
rescalings that map the canonical thermodynamics of the $\alpha$-model into
that of the mean field model. We also show that the chaotic properties of the
model, studied as a function of $\alpha$ display an universal behaviour.