Finite-size scaling in anisotropic systems

الأصل · EN

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⊥) 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 Lᵐ×∞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.