TY - JOUR

T1 - Low-temperature studies of random ising models

AU - Domb, C.

AU - Entin-Wohlman, O.

N1 - Funding Information:
We are grateful to Yrofessor H. Sompolinsky for suggesting the use of series expansions in this problem, and to Professor A. Aharony for helpful comments on the original manuscript. Financial help from the Israel Academy of Sciences and Humanities is gratefully acknowledged.

PY - 1984/8

Y1 - 1984/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0020797291&partnerID=8YFLogxK

U2 - 10.1080/13642818408238845

DO - 10.1080/13642818408238845

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AN - SCOPUS:0020797291

SN - 1364-2812

VL - 50

SP - 273

EP - 283

JO - Philosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties

JF - Philosophical Magazine B: Physics of Condensed Matter; Statistical Mechanics, Electronic, Optical and Magnetic Properties

IS - 2

ER -