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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
  • 13
    Citations
  • 0
    Usage
  • 8
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    13
    • Citation Indexes
      13
  • Captures
    8

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.

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