Exact solution of a classical short-range spin model with a phase transition in one dimension: The Potts model with invisible states

摘要

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: h(1) acting on a visible state and h(2) on an invisible state. We analyse its zeros in the complex-temperature plane in the case that h(1) = 0. When Im h(2) = 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 Im h(2) not equal 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. (C) 2017 Elsevier B.V. All rights reserved.