Abstract
The (d=2)-dimensional spin model composed of alternating strips of two different Ising magnets is revisited. Application of modern techniques results in explicit exact solution for the free energy and correlation lengths of the continuous (field-theoretic) limit of the model. In agreement with earlier results, the specific heat generally exhibitsthree different critical features: two near the respective critical temperaturesT c1 andT c2 of the composing models, as well as a new superlattice transition atT c1 <T c <T c2 . Further analysis shows that at all temperatures betweenT c1 andT c2 the correlations in the system include a low-amplitude but very long-range component reflecting fluctuations in a largescale domain wall network. The essential features of the solution can be explained by a reentrant dimensional crossover from thed=2, bulk behavior within the strips, to one-dimensional criticality in the individual strips, and finally back to the two-dimensional behavior on a new, superlattice level. This qualitative understanding of the physical content of the model allows for semiquantitative description of the temperature dependence of spontaneous magnetization and magnetic susceptibility, which have been previously obscure.
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Mikheev, L.V. Reentrant dimensional crossover in planar Ising superlattices. J Stat Phys 78, 79–101 (1995). https://doi.org/10.1007/BF02183339
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DOI: https://doi.org/10.1007/BF02183339