Ashkin–Teller model on a sequence of hierarchical lattices

S.S. Akimenko, A.V. Myshlyavtsev and M.D. Myshlyavtseva

Physica A: Statistical Mechanics and its Applications, 2023, vol. 620, issue C

Abstract: Some hierarchical lattices are able to imitate Bravais lattices, and in some cases it is possible to obtain an exact solution. For example, on folded square hierarchical lattices (FSHLs) one can obtain an exact solution even for rather complicated models such as the two-layer Ising model. But this model has a simple behavior, so we chose a similar model with a much more diverse phase behavior. In this work, we have studied the Ashkin–Teller model on the first two representatives of the FSHLs family. An additional calculation was carried out on a square lattice by tensor renormalization group for a more visual comparison of the results. Based on the calculation results, we have constructed phase diagrams for symmetric and asymmetric cases. As expected, the diagrams are qualitatively the same for square and hierarchical lattices. There are areas with a noticeable deviation, but in some places the result corresponds to the exact solution. The second occurs only where the critical values of the model are determined by logarithms of algebraic numbers.

Keywords: Ashkin–Teller model; Hierarchical lattice; Critical temperature; Renormalization group; Phase diagram; Tensor renormalization group (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:620:y:2023:i:c:s037843712300331x

DOI: 10.1016/j.physa.2023.128776

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