Abstract
We present the exact solution of the 1D classical shortrange 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 transfermatrix method, in the general case of two ordering fields: h_{1} acting on a visible state and h_{2} on an invisible state. We analyse its zeros in the complextemperature plane in the case that h_{1}=0. When Imh_{2}=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 Imh_{2}≠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 nonzero temperature.
Original language  English 

Pages (fromto)  35893593 
Number of pages  5 
Journal  Physics Letters, Section A: General, Atomic and Solid State Physics 
Volume  381 
Issue number  41 
Early online date  1 Sep 2017 
DOIs  
Publication status  Published  5 Nov 2017 
Keywords
 Invisible states
 Partition function zeros
 Phase transitions
 Potts model
ASJC Scopus subject areas
 Physics and Astronomy(all)
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Profiles

Ralph Kenna
 Research Centre for Fluid & Complex Systems  Professor of Theoretical Physics
Person: Teaching and Research