Nonuniversal finite-size scaling in anisotropic systems

Details Nonuniversal finite-size scaling in anisotropic systems Nonuniversal finite-size scaling in anisotropic systems

2004-08-24

arxiv.org/abs/cond-mat/0408511v3

Physics

Condensed Matter

Statistical Mechanics

8 pages, 1 figure, accepted for publication in Phys. Rev. E and modifications of text

Scientific paper

10.1103/PhysRevE.70.056136

We study the bulk and finite-size critical behavior of the O$(n)$ symmetric $\phi^4$ theory with spatially anisotropic interactions of non-cubic symmetry in $d<4$ dimensions. In such systems of a given $(d,n)$ universality class, two-scale factor universality is absent in bulk correlation functions, and finite-size scaling functions including the Privman-Fisher scaling form of the free energy, the Binder cumulant ratio and the Casimir amplitude are shown to be nonuniversal. In particular it is shown that, for anisotropic confined systems, isotropy cannot be restored by an anisotropic scale transformation.

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