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 journalArticlepeer-review


The authors 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. Their 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))) approximately mod p-pc mod , implying that the crossover exponent is Phi =1. 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) approximately Jalpha then, for p near pc, Tc(p) approximately mod p-pc mod 1 alpha /.

Original languageEnglish (US)
Article number010
Pages (from-to)L313-L318
JournalJournal of Physics A: General Physics
Issue number5
StatePublished - 1987

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Mathematical Physics


Dive into the research topics of 'The phase boundary in dilute and random Ising and Potts ferromagnets'. Together they form a unique fingerprint.

Cite this