The phase boundary in dilute and random Ising and Potts ferromagnets

M. Aizenmant, J. T. Chayes, L. Chayes, C. M. Newman

Research output: Contribution to journalArticle

Abstract

We present an approach to dilute Ising and Potts models, based on the Fortuin-Kasteleyn random cluster representation, which is simultaneously rigorous, intuitive and surprisingly simple. Our analysis yields, with no dimensional restrictions or other caveats, the following asymptotic form of the phase boundary. For the regular dilute model in which bonds have constant ferromagnetic coupling J with probability p and are vacant with probability 1 -p, the critical temperature scales as exp[-J/(kTc(p))]∼|p -pc|, implying that the crossover exponent is Φ = l. If the constant couplings are replaced by a distribution F(J) with mass near J = 0, quite different crossover behaviour is observed. For example, if F(J)∼J α then, for p near pc, Tc(p)∼|p- pc|1/α

Original languageEnglish (US)
JournalJournal of Physics A: Mathematical and General
Volume20
Issue number5
DOIs
StatePublished - Apr 1 1987

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Ferromagnet
Phase boundaries
Ising
Crossover
crossovers
Potts model
Temperature scales
Ising model
temperature scales
Potts Model
Critical Temperature
Ising Model
Intuitive
constrictions
critical temperature
Exponent
exponents
Model-based
Restriction
Model

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

The phase boundary in dilute and random Ising and Potts ferromagnets. / Aizenmant, M.; Chayes, J. T.; Chayes, L.; Newman, C. M.

In: Journal of Physics A: Mathematical and General, Vol. 20, No. 5, 01.04.1987.

Research output: Contribution to journalArticle

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