Potts Models with (17) Invisible States on Thin Graphs

Abstract

The order of a phase transition is usually determined by the nature of the symmetry breaking at the phase transition point and the dimension of the model under consideration. For instance, q-state Potts models in two dimensions display a second order, continuous transition for q = 2,3,4 and first order for higher q. Tamura et al recently introduced Potts models with "invisible" states which contribute to the entropy but not the internal energy and noted that adding such invisible states could transmute continuous transitions into first order transitions. This was observed both in a Bragg-Williams type mean-field calculation and 2D Monte-Carlo simulations. It was suggested that the invisible state mechanism for transmuting the order of a transition might play a role where transition orders inconsistent with the usual scheme had been observed. In this paper we note that an alternative mean-field approach employing 3-regular random ("thin") graphs also displays this change in the order of the transition as the number of invisible states is varied, although the number of states required to effect the transmutation, 17 invisible states when there are 2 visible states, is much higher than in the Bragg-Williams case. The calculation proceeds by using the equivalence of the Potts model with 2 visible and r invisible states to the Blume-Emery-Griffiths (BEG) model, so a by-product is the solution of the BEG model on thin random graphs.

(2) Minor typos corrected, references updated

References in corpus (4)

• Quadrupolar correlations and spin freezing in S = 1 triangular lattice antiferromagnets
• Structure of Metastable States in Phase Transitions with High-Spin Low-Spin Degree of Freedom
• Phase Transition in Potts Model with Invisible States
• Potts model with invisible colours: Random-cluster representation and Pirogov-Sinai analysis

Cited by in corpus (7)

• Exact solution of a classical short-range spin model with a phase transition in one dimension: the Potts model with invisible states
• Potts Model with Invisible States: A Review
• Classical phase transitions in a one-dimensional short-range spin model induced by entropy depletion or complex fields
• Potts Models with Invisible States on General Bethe Lattices
• Marginal dimensions of the Potts model with invisible states
• Ising model with invisible states on scale-free networks
• Changeover phenomenon in randomly colored Potts models