Exact solution of a classical short-range spin model with a phase transition in one dimension: The Potts model with invisible states
Physics Letters A, ISSN: 0375-9601, Vol: 381, Issue: 41, Page: 3589-3593
2017
- 13Citations
- 8Captures
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Article Description
We present the exact solution of the 1D classical short-range Potts model with invisible states. Besides the q states of the ordinary Potts model, this possesses r additional states which contribute to the entropy, but not to the interaction energy. We determine the partition function, using the transfer-matrix method, in the general case of two ordering fields: h1 acting on a visible state and h2 on an invisible state. We analyse its zeros in the complex-temperature plane in the case that h1=0. When Imh2=0 and r≥0, these zeros accumulate along a line that intersects the real temperature axis at the origin. This corresponds to the usual “phase transition” in a 1D system. However, for Imh2≠0 or r<0, the line of zeros intersects the positive part of the real temperature axis, which signals the existence of a phase transition at non-zero temperature.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S037596011730837X; http://dx.doi.org/10.1016/j.physleta.2017.08.063; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85028988102&origin=inward; https://linkinghub.elsevier.com/retrieve/pii/S037596011730837X; https://dx.doi.org/10.1016/j.physleta.2017.08.063
Elsevier BV
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