Square-lattice random potts model: Criticality and pitchfork bifurcation

1984 ◽  
Vol 128 (1-2) ◽  
pp. 207-228 ◽  
Author(s):  
Uriel M.S. Costa ◽  
Constantino Tsallis
Keyword(s):  
Potts Model ◽  
Pitchfork Bifurcation ◽  
Square Lattice

Critical antiferromagnetic square-lattice Potts model

1982 ◽  
Vol 383 (1784) ◽  
pp. 43-54 ◽  
Keyword(s):  
Free Energy ◽  
Critical Temperature ◽  
Internal Energy ◽  
Latent Heat ◽  
Potts Model ◽  
Square Lattice ◽  
Isotropic Model ◽  
First Order

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 .

scholarly journals The antiferromagnetic transition for the square-lattice Potts model

2006 ◽  
Vol 743 (3) ◽  
pp. 207-248 ◽  
Author(s):  
Jesper L. Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Potts Model ◽  
Square Lattice ◽  
Antiferromagnetic Transition

Free-fermion, checkerboard and Z -invariant lattice models in statistical mechanics

1986 ◽  
Vol 404 (1826) ◽  
pp. 1-33 ◽  
Keyword(s):  
Ising Model ◽  
Potts Model ◽  
Three Dimensional ◽  
Lattice Models ◽  
Square Lattice ◽  
Free Fermion ◽  
Local Correlations ◽  
Free Fermion Model ◽  
Zamolodchikov Model ◽  
Special Case

It is shown that the two-dimensional free fermion model is equivalent to a checkerboard Ising model, which is a special case of the general ‘ Z -invariant’ Ising model. Expressions are given for the partition function and local correlations in terms of those of the regular square lattice Ising model. Corresponding results are given for the self-dual Potts model, and the application of the methods to the three-dimensional Zamolodchikov model is discussed. The paper ends with a discussion of the critical and disorder surfaces of the checkerboard Potts model.

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