Abstract
Various thermal equilibrium and nonequilibrium phase transitions exist where the correlation lengths in different lattice directions diverge with different exponentsv ‖,v ⊥: uniaxial Lifshitz points, the Kawasaki spin exchange model driven by an electric field, etc. An extension of finite-size scaling concepts to such anisotropic situations is proposed, including a discussion of (generalized) rectangular geometries, with linear dimensionL ‖ in the special direction and linear dimensionsL ⊥ in all other directions. The related shape effects forL ‖≠L ⊥ but isotropic critical points are also discussed. Particular attention is paid to the case where the generalized hyperscaling relationv ‖+(d−1)v ⊥=γ+2β does not hold. As a test of these ideas, a Monte Carlo simulation study for shape effects at isotropic critical point in the two-dimensional Ising model is presented, considering subsystems of a 1024x1024 square lattice at criticality.
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Visiting Supercomputer Senior Scientist at Rutgers University.
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Binder, K., Wang, J.S. Finite-size effects at critical points with anisotropic correlations: Phenomenological scaling theory and Monte Carlo simulations. J Stat Phys 55, 87–126 (1989). https://doi.org/10.1007/BF01042592
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DOI: https://doi.org/10.1007/BF01042592