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Physics Letters A

Reentrant phase transitions in the two-dimensional Ising model with competing nearest neighbour interactions

Hidetsugu Kitatani, Seiji Miyashita, Masuo Suzuki

Published Mar 1, 1985• 38 citations
Publisher
DOI
10.1016/0375-9601(85)90827-8

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The critical behaviour of an Ising model with competing first- and third-nearest-neighbour interactions ('biaxial next-nearest-neighbour Ising' or BNNNI model) on the square lattice is investigated by finite lattice methods. In the ferromagnetic region, the phase boundary is located with an accuracy at least equal to that of alternative methods. In the antiphase region, distinctive structure in finite lattice estimators is found over an extended temperature range. However, the nature of the transition remains unclear.
Abstract The mixed spin‐(1/2, S ) Ising model on the Union Jack (centered square) lattice is investigated by establishing the mapping relationship with its corresponding eight‐vertex model. An interplay between the nearest‐neighbour interaction, the competing next‐nearest‐neighbour interaction and the single‐ion anisotropy gives rise to a rather complex critical behaviour displayed in the reentrant phase transitions, the weak universal critical behaviour, as well as, a presence of first‐ and second‐order phase transitions. The most interesting finding to emerge from the present study relates to a variation of the weak‐universal critical exponents along the line of bicritical points, which is being twice as large for the mixed spin‐(1/2, S ) systems with the integer spin‐S atoms as for the ones with the half‐odd‐integer spin‐S atoms. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)