Geometric critical exponent inequalities for general random cluster models
Journal Article
·
· J. Stat. Phys.; (United States)
A set of new critical exponent inequalities, d(1-1/delta) greater than or equal to 2 - eta, dv(1-1/delta) greater than or equal to ..gamma.., and d..mu.. greater than or equal to 1, is proved for a general class of random cluster models, which includes (independent or dependent) percolations, lattice animals (with any interactions), and various stochastic cluster growth models. The inequalities imply that the critical phenomena in the models are inevitably not mean-field-like in the dimensions one, two, and three.
- Research Organization:
- Princeton Univ., NJ (USA)
- OSTI ID:
- 5300446
- Journal Information:
- J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 49:3/4; ISSN JSTPB
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CRITICAL TEMPERATURE
CRYSTAL LATTICES
CRYSTAL MODELS
CRYSTAL STRUCTURE
DIFFUSION
DISTRIBUTION FUNCTIONS
FERROMAGNETISM
FUNCTIONS
GEOMETRY
MAGNETISM
MATHEMATICAL MODELS
MATHEMATICS
MEAN-FIELD THEORY
MECHANICS
ONE-DIMENSIONAL CALCULATIONS
ORDER-DISORDER TRANSFORMATIONS
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
RANDOMNESS
SPIN GLASS STATE
STATISTICAL MECHANICS
THERMODYNAMIC PROPERTIES
THREE-DIMENSIONAL CALCULATIONS
TRANSITION TEMPERATURE
TWO-DIMENSIONAL CALCULATIONS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CRITICAL TEMPERATURE
CRYSTAL LATTICES
CRYSTAL MODELS
CRYSTAL STRUCTURE
DIFFUSION
DISTRIBUTION FUNCTIONS
FERROMAGNETISM
FUNCTIONS
GEOMETRY
MAGNETISM
MATHEMATICAL MODELS
MATHEMATICS
MEAN-FIELD THEORY
MECHANICS
ONE-DIMENSIONAL CALCULATIONS
ORDER-DISORDER TRANSFORMATIONS
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
RANDOMNESS
SPIN GLASS STATE
STATISTICAL MECHANICS
THERMODYNAMIC PROPERTIES
THREE-DIMENSIONAL CALCULATIONS
TRANSITION TEMPERATURE
TWO-DIMENSIONAL CALCULATIONS