Journal ArticleDOI
Critical antiferromagnetic square-lattice Potts model
R. J. Baxter
- Vol. 383, Iss: 1784, pp 43-54
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In this article, the critical temperature of the antiferromagnetic q-state Potts model on the square lattice is located, and the critical free energy and internal energy are evaluated.Abstract:
The critical temperature of the antiferromagnetic q -state Potts model on the square lattice is located, and the critical free energy and internal energy are evaluated. As with the ferromagnetic model, the transition is continuous for q ≼4, and its first-order (i. e. has latent heat) for q >4. However, only for q ≼3 can the critical temperature be real. For the isotropic model the criticality condition is exp( J / k T ) = -1 + (4- q ) ½ .read more
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Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem
Jesús Salas,Alan D. Sokal +1 more
TL;DR: In this paper, it was shown that the q-state Potts antiferromagnet on a lattice of maximum coordination number r exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever q>2r.
Journal ArticleDOI
Exact Potts Model Partition Functions on Ladder Graphs
Robert Shrock,Robert Shrock +1 more
TL;DR: In this paper, exact calculations of the partition function Z of the q-state Potts model and its generalization to real q, for arbitrary temperature on n-vertex ladder graphs, with free, cyclic, and Mobius longitudinal boundary conditions, were presented.
Journal ArticleDOI
The antiferromagnetic transition for the square-lattice Potts model
TL;DR: In this article, the problem of the antiferromagnetic transition for the Q-state Potts model (defined geometrically for Q generic using the loop/cluster expansion) on the square lattice was solved based on the detailed analysis of the Bethe ansatz equations.
Journal ArticleDOI
High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials
TL;DR: In this paper, Jacobsen and Scullard proposed a more efficient transfer matrix approach based on a formulation within the periodic Temperley-Lieb algebra for the q-state Potts model.
Journal ArticleDOI
Potts model of magnetism (invited)
TL;DR: In this article, the authors review the properties of the Potts model as a model of magnetism and present some exact and rigorous results for both the ferromagnetic and antiferromagnetic models.
References
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Journal ArticleDOI
Partition function of the eight vertex lattice model
TL;DR: In this paper, the partition function of the zero-field eight-vertices model on a square M by N lattice is calculated exactly in the limit of M, N large.
Journal ArticleDOI
Fundamental Problems in Statistical Mechanics
E. G. D. Cohen,Nandor L. Balazs +1 more
Journal ArticleDOI
Potts model at the critical temperature
TL;DR: In this article, it was shown that the two-dimensional q-component Potts model is equivalent to a staggered ice-type model, and it was deduced that the model has a first-order phase transition for q>4, and a higher-order transition for Q
Journal ArticleDOI
Solvable eight-vertex model on an arbitrary planar lattice
TL;DR: In this paper, it was shown that the Kagome lattice model can be solved exactly in the thermodynamic limit, its local properties at a particular site being those of a related square lattice.
Journal ArticleDOI
Exact Solution of the F Model of An Antiferroelectric
TL;DR: In this paper, an extension of the method used to find the residual entropy of square ice was used to solve the two-dimensional Ising model for an antiferromagnet.