Griffiths singularities in random magnets: Results for a soluble model

Journal Article · Sun Oct 01 04:00:00 EDT 1989 · Physical Review (Section) B: Condensed Matter; (USA)

DOI:https://doi.org/10.1103/PhysRevB.40.6980· OSTI ID:5470262

Bray, A J; Huifang, D ^[1]

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1. Department of Theoretical Physics, The University, Manchester M139PL, England (GB)

A soluble, but nontrivial, model of a dilute Ising ferromagnet is studied, with infinite-range interactions but finite average connectivity {ital c}. The density of (Yang-Lee) zeros of the partition function in the complex {ital z}=exp({minus}2{ital H}) plane (where {ital H} is the external magnetic field in units of the temperature) is calculated explicitly in the high-temperature phase for large but finite {ital c} and small {vert bar}{ital H}{vert bar}. The density of zeros on the unit circle {ital H}={ital i}{theta} has the form {rho}({theta}){similar to}exp{l brace}{minus}({ital cf}({ital K})/{vert bar}{theta}{vert bar})ln (1/{vert bar}{theta}{vert bar}){r brace} for {vert bar}{theta}{vert bar}{r arrow}0. The function {ital f}({ital K}) ({ital K}={ital J}/{ital T}) vanishes at the critical coupling {ital K}{sub {ital C}}(c). Heuristic arguments are given for the form of {rho}({theta}) expected for systems with short-range interactions.

• OSTI ID: 5470262
• Journal Information: Physical Review (Section) B: Condensed Matter; (USA), Journal Name: Physical Review (Section) B: Condensed Matter; (USA) Vol. 40:10; ISSN PRBMD; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

656002* -- Condensed Matter Physics-- General Techniques in Condensed Matter-- (1987-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CRYSTAL MODELS
FERROMAGNETIC MATERIALS
FUNCTIONS
ISING MODEL
MAGNETIC MATERIALS
MAGNETIZATION
MATERIALS
MATHEMATICAL MODELS
MEAN-FIELD THEORY
ORDER PARAMETERS
PARTITION FUNCTIONS
PHYSICAL PROPERTIES
RELAXATION
THERMODYNAMIC PROPERTIES