Journal ArticleDOI
The dilute random-bond Potts model
B. W. Southern,Michael Thorpe +1 more
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In this paper, it was shown that the phase boundary of the Potts model is related to the bond percolation problem, and that it behaves as exp(sK)=(ln s)/(s-1/(p-pc/pc) for all 2-D lattices.Abstract:
Some of the properties of the bond diluted s-state Potts model are examined in this paper, and in particular the phase boundary It is shown that as s to 1, the model is simply related to the bond percolation problem By extending the replica arguments of Domany (1978) (which are probably exact), it is shown that near p, the phase boundary behaves as exp(-sK)=(ln s)/(s-1)(p-pc/pc) for all 2-D lattices The authors also construct a coherent potential approximation that is exact for all lattices as s to 1, and for arbitrary s on Bethe latticesread more
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The Potts model
TL;DR: In this paper, a tutorial review on the Potts model is presented aimed at bringing out the essential and important properties of the standard Potts models, focusing on exact and rigorous results, but other aspects of the problem are also described to achieve a unified perspective.
Journal ArticleDOI
The Potts model on Bethe lattices. I. General results
TL;DR: In this article, the q-state ferromagnetic Potts model (FPM) and antiferromagnetic potts model were solved on Bethe lattices for all values of the external magnetic field and temperature, and exact expressions of all thermodynamic functions of interest in the FPM and APM were calculated.
Journal ArticleDOI
Aggregation and intermediate phases in dilute spin systems
TL;DR: In this paper, the authors studied a variety of dilute annealed lattice spin systems and uncovered a new phase characterized by the occupation and vacancy of staggered sublattices.
Journal ArticleDOI
Pure and dilute Z(N) spin and generalised gauge lattice systems: duality and criticality
F C Alcaraz,C Tsallis +1 more
TL;DR: In this article, the authors considered the pure Z(N) spin systems, including the standard Ising and Potts models, as well as generalised gauge systems (plaquettes or more complex simplex) in d-dimensional hypercubic lattices.
Journal ArticleDOI
Percolative phase transition in a disordered Ising model with finite disorder correlation length
TL;DR: In this paper, the phase transition in an Ising model with correlated disorder is discussed, and two parameters describe the disorder: its variance and its finite correlation lengthscale, and the dominating lengthscale is not the correlation length of thermal fluctuations but the connectivity length of ordered regions.
References
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Book
Phase Transitions and Critical Phenomena
TL;DR: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results as discussed by the authors, and the major aim of this serial is to provide review articles that can serve as standard references for research workers in the field.
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
Critical properties of many-component systems
TL;DR: In this paper, it is shown that there is an integral representation for the partition function which reduces n to an explicit parameter in an averaged partition function for the m-component model, leading to a simple discussion of properties of the system as a function of n.
Journal ArticleDOI
Triangular Potts model at its transition temperature, and related models
TL;DR: In this article, it was shown that this is equivalent to a restricted six-vertex model on the Kagome lattice, and to the g-state triangular (or hexagonal) Potts model at its transition temperature T c.
Journal ArticleDOI
Duality transformation in a many‐component spin model
F. Y. Wu,Y. K. Wang +1 more
TL;DR: It is shown that the duality transformation relates a spin model to its dual whose Boltzmann factors are the eigenvalues of the matrix formed by the Boltzman factors of the original spin model.