Abstract
We study inhomogeneous two-dimensional Ising models with a random distribution of ferro- and antiferromagnetic couplings,K ij =±K, or equivalently a random distribution of frustrations. In particular, we considerRandom Layered Frustration models (RLF) where randomness is confined to the vertical direction. These RLF-models are solved exactly, i.e., partition function and free energy are obtained in closed form for an arbitrary random distribution of finite period. The phase transition is of Ising type. A simple formula for the transition temperature is derived which depends only on the mean coupling\(\overline {K_{ij} } \), but not on other details of the distribution. Both cases,T c =0 andT c ≠0, are possible. Groundstate energy and groundstate degeneracy, or equivalently the rest entropy, are determined. It is found that both the occurence or absence of a phase transition may be accompanied with vanishing or nonvanishing rest entropy. We also show that for the RLF-models a phase transition is excluded when all groundstates are connected with one another by local transformations which presumably holds generally. A remarkable result is that the transition of the ferromagnetic Ising model can be destroyed completely if one replaces an arbitrarily small fraction of ferromagnetic couplings by antiferromagnetic ones in a suitable way.
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Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln
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Hoever, P., Wolff, W.F. & Zittartz, J. Random layered frustration models. Z. Physik B - Condensed Matter 41, 43–53 (1981). https://doi.org/10.1007/BF01301409
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DOI: https://doi.org/10.1007/BF01301409