Universal finite-size scaling amplitudes in anisotropic scaling

Abstract

Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that translation invariance and hyperscaling are valid, the Privman-Fisher scaling form of isotropic equilibrium phase transitions is readily generalized. For non-equilibrium systems, universality is shown analytically for directed percolation and is tested numerically in the annihilation-coagulation model and in the pair contact process with diffusion. In these models, for both periodic and free boundary conditions, the universality of the finite-size scaling amplitude of the leading relaxation time is checked. Amplitude universality reveals strong transient effects along the active-inactive transition line in the pair contact process.

16 pages, Latex, 2 figures, final version, to appear in J. Phys. A

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Cited by in corpus (27)

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• The density-matrix renormalization group
• The Importance of being Odd
• The non-equilibrium phase transition of the pair-contact process with diffusion
• Nonuniversal finite-size scaling in anisotropic systems
• Towards Classification of Phase Transitions in Reaction--Diffusion Models
• On the critical behavior of the one dimensional, diffusive pair contact process
• Nonuniversality in the pair contact process with diffusion
• Pair Contact Process with Diffusion: Failure of Master Equation Field Theory
• On the choice of the density matrix in the stochastic TMRG
• Phase transition of a two dimensional binary spreading model
• Macroscopic Time-Reversal Symmetry Breaking at Nonequilibrium Phase Transition
• On the Symmetry of Universal Finite-Size Scaling Functions in Anisotropic Systems
• Phase transition classes in triplet and quadruplet reaction diffusion models
• 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
• Strongly anisotropic non-equilibrium phase transition in Ising models with friction
• Multicomponent binary spreading process
• Stochastic cellular automaton for the coagulation-fission-process 2A->3A, 2A->A
• Monte-Carlo study of anisotropic scaling generated by disorder
• Sheared Ising models in three dimensions
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• Phase transitions of the binary production 2A->3A, 4A->0 model
• A coupled two-species model for the pair contact process with diffusion
• Random sparse generators of Markovian evolution and their spectral properties
• An efficient perturbation theory of density matrix renormalization group