Some rigorous results on majority rule renormalization group transformations near the critical point

Journal Article · Thu Jul 01 00:00:00 EDT 1993 · Journal of Statistical Physics; (United States)

DOI:https://doi.org/10.1007/BF01048038· OSTI ID:5719203

Kennedy, T ^[1]

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1. Univ. of Arizona, Tucson (United States)

The authors consider the majority rule renormalization group transformation with two-by-two blocks for the Ising model on a two-dimensional square lattice. For three particular choices of the block spin configuration it is proven that the model conditioned on the block spin configuration remains in the high-temperature phrase even when the temperature is slightly below the critical temperature of the ordinary Ising model with no conditioning. The authors take as the definition of the infinite-volume limit an equation introduced in earlier work by the author. A computer is used to find an approximate solution of this equation and verify a condition which implies the existence of an exact solution. 13 refs., 2 figs., 1 tab.

• OSTI ID: 5719203
• Journal Information: Journal of Statistical Physics; (United States), Vol. 72:1-2; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
36 MATERIALS SCIENCE
CRYSTAL LATTICES
LATTICE FIELD THEORY
CRYSTAL-PHASE TRANSFORMATIONS
CRITICAL TEMPERATURE
ISING MODEL
COMPUTER CALCULATIONS
RENORMALIZATION
SPIN
STATISTICAL MODELS
TEMPERATURE DEPENDENCE
ANGULAR MOMENTUM
CRYSTAL MODELS
CRYSTAL STRUCTURE
FIELD THEORIES
MATHEMATICAL MODELS
PARTICLE PROPERTIES
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
THERMODYNAMIC PROPERTIES
TRANSITION TEMPERATURE
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)
360602 - Other Materials- Structure & Phase Studies