Shape dependence of the finite-size scaling limit in a strongly anisotropic $O(\infty )$ model

Abstract

We discuss the shape dependence of the finite-size scaling limit in a strongly anisotropic O(N) model in the large-N limit. We show that scaling is observed even if an incorrect value for the anisotropy exponent is considered. However, the related exponents may only be effective ones, differing from the correct critical exponents of the model. We discuss the implications of our results for numerical finite-size scaling studies of strongly anisotropic systems.

arXiv comment21 pages, 4 figures

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• Quantum phase transition in the spin-anisotropic quantum spherical model
• Generalized Mittag-Leffler functions in the theory of finite-size scaling for systems with strong anisotropy and/or long-range interaction
• Critical Behavior of the Two-Dimensional Randomly Driven Lattice Gas
• Short-time Behaviour and Criticality of Driven Lattice Gases
• Dynamical symmetries in the non-equilibrium dynamics of the directed spherical model