Lack of re-entrance in certain Ising spin-glass models

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Abstract
The authors report results of numerical transfer matrix calculations on a dilute two-dimensional first- and second-neighbour Ising model and Migdal-Kadanoff renormalisation group studies on a random nearest-neighbour Ising model in two and three dimensions. The calculations were carried out to examine the existence of reentrance in these systems, defined by the disappearance of long-range ferromagnetic order upon lowering the temperature. They find, contrary to other claims in the literature, that there is no reentrance in these models or, at best, reentrance occurs over a very narrow range of parameters, and speculate about the necessary ingredients to obtain reentrance in random spin systems.