CRITICAL BEHAVIOR OF SEVERAL LATTICE MODELS WITH LONG-RANGE INTERACTION

被引:38
作者
KAC, M
THOMPSON, CJ
机构
[1] Rockefeller University, New York, NY
[2] Applied Mathematics Department, University of New South Wales, Kensington, NSW
[3] Applied Mathematics Department, Massachusetts Institute of Technology, Cambridge
[4] Northwestern University, Evanston, IL
关键词
D O I
10.1063/1.1664976
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We consider a one-dimensional model with infinite-range interaction, a two-dimensional model, and a three-dimensional model, whose free energies can be expressed in terms of the largest eigenvalue of an integral equation. High- and low-temperature expansions in powers of the reciprocal of the range of the exponential part of the interaction, with the classical Curie-Weiss theory as leading term, are developed and studied in the critical region. We find that to leading order in the critical region the resummed high-and low-temperature expansions are analytic at the classical critical point but are nonanalytic at a displaced critical point. The modified singularities, which are no longer of Curie-Weiss type, give critical exponents which are identical with those obtained by Brout and others, and are almost surely not the true exponents. The technique, however, suggests a possible general method of successive approximation to true critical behavior.
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页码:1373 / &
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