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.
|Number of pages||5|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|Early online date||1 Sep 2017|
|Publication status||Published - 5 Nov 2017|
- Invisible states
- Partition function zeros
- Phase transitions
- Potts model
ASJC Scopus subject areas
- Physics and Astronomy(all)
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- Research Centre for Fluid and Complex Systems - Professor of Theoretical Physics
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