Low-temperature studies of random ising models

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A brief discussion is given of the application of the methods of low-temperature or excitation expansions to random Iaing models. A specific investigation is then undertaken of the low-temperature behaviour of the random-field model A relationship is established between the δ-function distribution with equal probabilities of positive and negative fixed fields H0and a site percolation process on the lattice with p= ½. At T = 0 successive percolation clusters give rise to first-order transitions at different values of H0 There is a significant difference in behaviour between lattices for which pc < ½ which have an infinite cluster and pc > ½ which do not. For standard lattices, no matter how small is H0 there are overturned clusters, but for the Bethe lattice there is a range of H0 for which the ground state is one of ferromagnetic order. By allowing the coordination number to become large in the latter system, the results of the mean-field approximation are reproduced. The above considerations do not apply to a Gaussian distribution of fields, and the absence of a first-order transition can then be understood. Since large clusters overturn for small fields, there are clear indications of metastable behaviour.

Original languageEnglish
Pages (from-to)273-283
Number of pages11
JournalPhilosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties
Issue number2
StatePublished - 1 Jan 1984
Externally publishedYes

ASJC Scopus subject areas

  • General Chemical Engineering
  • General Physics and Astronomy


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