Phase transition in a general class of Ising-type models is sharp

Journal Article · Fri May 01 04:00:00 EDT 1987 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01007515· OSTI ID:6262612

Aizenman, M; Barsky, D J; Fernandez, R

For a family of translation-invariant, ferromagnetic, one-component spin systems - which includes Ising and phi/sup 4/ models - they prove that (i) the phase transition is sharp in the sense that at zero magnetic field the high- and low-temperature phases extend up to a common critical point, and (ii) the critical exponent ..beta.. obeys the mean field bound ..beta.. less than or equal to 1/2. The present derivation of these nonperturbative statements is not restricted to regular systems, and is based on a new differential inequality whose Ising model version is M less than or equal to ..beta..h/sub chi/ + M/sup 3/ + ..beta..M/sup 2/ deltaM/delta..beta... The significance of the inequality was recognized in a recent work on related problems for percolation models, while the inequality itself is related to previous results, by a number of authors, on ferromagnetic and percolation models.

• Research Organization: Rutgers, The State Univ. of New Jersey, New Brunswick
• OSTI ID: 6262612
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 47:3-4; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

645400 -- High Energy Physics-- Field Theory
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
COUPLING
COUPLING CONSTANTS
CRYSTAL LATTICES
CRYSTAL MODELS
CRYSTAL STRUCTURE
EXPECTATION VALUE
FERROMAGNETISM
FIELD THEORIES
HAMILTONIANS
INTERMEDIATE COUPLING
INVARIANCE PRINCIPLES
ISING MODEL
J-J COUPLING
L-S COUPLING
MAGNETIC FIELDS
MAGNETIC PROPERTIES
MAGNETIC SUSCEPTIBILITY
MAGNETISM
MAGNETIZATION
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MEAN-FIELD THEORY
MECHANICS
PARTICLE PROPERTIES
PHASE TRANSFORMATIONS
PHI4-FIELD THEORY
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
RANDOMNESS
SPIN
STATISTICAL MECHANICS