Finite-size effects at critical points with anisotropic correlations: Phenomenological scaling theory and Monte Carlo simulations

Journal Article · Sat Apr 01 00:00:00 EST 1989 · Journal of Statistical Physics; (USA)

DOI:https://doi.org/10.1007/BF01042592· OSTI ID:5589726

Binder, K; Wang, Jiansheng ^[1]

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1. Rutgers, The State Univ. of New Jersey, New Brunswick (USA)

Various thermal equilibrium and nonequilibrium phase transitions exist where the correlation lengths in different lattice directions diverge with different exponents {nu}{sub {parallel}}, {nu}{sub {perpendicular}}: 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 dimension L{sub {parallel}} in the special direction and linear dimensions L{sub {perpendicular}} in all other directions. The related shape effects for L{sub {parallel}} {ne} L{sub {perpendicular}} but isotropic critical points are also discussed. Particular attention is paid to the case where the generalized hyperscaling relation {nu}{sub {parallel}} + (d {minus} 1) {nu}{sub {perpendicular}} = {gamma} + 2{beta} 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 1024 {times} 1024 square lattice at criticality.

• OSTI ID: 5589726
• Journal Information: Journal of Statistical Physics; (USA), Vol. 55:1-2; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CRYSTAL MODELS
SCALING LAWS
ANISOTROPY
COMPUTERIZED SIMULATION
CRITICAL PRESSURE
CRITICAL TEMPERATURE
CRYSTAL LATTICES
EQUILIBRIUM
FEYNMAN PATH INTEGRAL
ISING MODEL
MAGNETIZATION
MEAN-FIELD THEORY
MONTE CARLO METHOD
PHASE TRANSFORMATIONS
SHAPE
SPIN
SPIN EXCHANGE
STATISTICAL MECHANICS
ANGULAR MOMENTUM
CRYSTAL STRUCTURE
INTEGRALS
MATHEMATICAL MODELS
MECHANICS
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
SIMULATION
THERMODYNAMIC PROPERTIES
TRANSITION TEMPERATURE
656002* - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-)
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics
645400 - High Energy Physics- Field Theory