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Finite-size scaling in anisotropic systems

N. S. Tonchev
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Abstract

We present analytical results for the finite-size scaling in d--dimensional O(N) systems with strong anisotropy where the critical exponents (e.g. ν_{||} and ν_{\perp}) depend on the direction. Prominent examples are systems with long-range interactions, decaying with the interparticle distance r as r^{-d-σ} with different exponents σin corresponding spatial directions, systems with space-"time"a anisotropy near a quantum critical point and systems with Lifshitz points. The anisotropic properties involve also the geometry of the systems. We consider systems confined to a d-dimensional layer with geometry L^{m}\times\infty^{n}; m+n=d and periodic boundary conditions across the finite m dimensions. The arising difficulties are avoided using a technics of calculations based on the analytical properties of the generalized Mittag-Leffler functions.

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N. S. Tonchev. 2005-12-07. Finite-size scaling in anisotropic systems. https://arxiv.org/abs/cond-mat/0512146

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