Non-Universal Finite Size Effects with Universal Infinite-Size Free Energy for the $α$-XY model

Details Non-Universal Finite Size Effects with Universal Infinite-Size Free Energy for the $α$-XY model Non-Universal Finite Size Effects with Universal Infinite-Size Free Energy for the $α$-XY model

2005-12-16

arxiv.org/abs/cond-mat/0512381v1

Physics

Condensed Matter

Statistical Mechanics

Proceedings of the workshop Comlexty and Nonextensivity - New Trends in Statistical Mechancs - (CN-Kyoto)

Scientific paper

10.1016/j.physa.2005.02.044

We study finite size effects in a family of systems in which a parameter controls interaction-range. In the long-range regime where the infinite-size free energy is universal, we show that the finite size effects are not universal but depend on the interaction-range. The finite size effects are observed through discrepancies between time-averages of macroscopic variables in Hamiltonian dynamics and canonical averages of ones with infinite degrees of freedom. For a high energy regime, the relation to a pair of the discrepancies is theoretically predicted and numerically confirmed. We also numerically show that the finite-size effects of macroscopic variables in the canonical ensemble are close to ones in the dynamical systems.

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