Hu CK, Izmailian NS, Oganesyan KB. Exact phase diagrams for an Ising model on a two-layer Bethe lattice.
PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999;
59:6489-96. [PMID:
11969634 DOI:
10.1103/physreve.59.6489]
[Citation(s) in RCA: 63] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/1998] [Revised: 02/17/1999] [Indexed: 11/07/2022]
Abstract
Using an iteration technique, we obtain exact expressions for the free energy and the magnetization of an Ising model on a two-layer Bethe lattice with intralayer coupling constants J1 and J2 for the first and the second layer, respectively, and interlayer coupling constant J3 between the two layers; the Ising spins also couple with external magnetic fields, which are different in the two layers. We obtain exact phase diagrams for the system and find that when /J3/-->0, DeltaT(c) identical with[T(c)(J3)-T(c)(0)]/T(c)(0) approximately [J3]/J(1)/(1/psi), where T(c)(J3) is the phase-transition temperature for the system with interlayer coupling constant J3 and the shift exponent psi is 1 for J(1)=J(2) and is 0.5 for J1 not equal to J2. Such results are consistent with predictions of a scaling theory. We also derive equations for DeltaT(c) when /J3/ approaches infinity.
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