Showing papers on "Potts model published in 1974"
TL;DR: In this article, the exact transition temperature of the Potts model with q states per site was obtained for the triangular and honeycomb lattices by using duality and star-triangle transformations together with a uniqueness assumption.
Abstract: By the use of duality and star-triangle transformations together with a uniqueness assumption, the exact transition temperature of the Potts model with q states per site is obtained for the triangular and honeycomb lattices.
78 citations
TL;DR: In this paper, a mean-field theory of the q-component Potts model is given, and the transition is first order for q>or=3, where q is the number of components.
Abstract: A mean-field theory of the q-component Potts model is given. The transition is first order for q>or=3. For large q the mean-field results agree with all the known exact results in two dimensions for the Potts model. It is conjectured that the mean-field theory provides an accurate description of the transition in two or higher dimensions when the number of components is large.
73 citations
TL;DR: In this article, the authors derived the partition functions for the q-state two-level model and the planar planar Potts model for the star topology and showed that the partition function depends only on the topology of the star and not on any two-degree vertices.
Abstract: Eigenvalues and eigenvectors are derived for the q-state two-level model introduced by Potts in 1952, and it is shown that for any net the partition function depends only on the topology and not on any two-degree vertices. This enables a simple method to be used calculating the partition functions of standard star topologies. The second q-orientation model introduced by Potts (termed the planar Potts model) is discussed, and it is shown that the same property holds. Partition functions for certain star topologies are derived for this model. By considering the asymptotic form of the coefficients in high-temperature expansions of the partition function, estimates are obtained of the critical temperatures of these models in terms of the geometrical properties of self-avoiding walks.
55 citations
TL;DR: In this paper, high-field expansions are obtained for the three-state Potts model on a square lattice, and the general properties of the transition in face-centred cubic systems are investigated.
Abstract: High-field expansions are obtained for the three-state Potts model. These expansions are used to investigate the critical isotherm of the three-state system on a square lattice, and to determine the general properties of the transition in face-centred cubic systems.
43 citations
TL;DR: In this paper, the thermodynamic functions for the three-component Potts model on a simple cubic lattice are constructed as a low-temperature, high-field series and also as a high- temperature, low field series, which may be evidence for a continuous phase transition.
Abstract: The thermodynamic functions for the three-component Potts model on a simple cubic lattice are constructed as a low-temperature, high-field series and also as a high-temperature, low-field series. Both series predict divergences in the relevant compliances in the same temperature range, which may be evidence for a continuous phase transition. The critical exponents are tentatively determined, and related to a proposed theory for the Potts tricritical point.
40 citations
TL;DR: The susceptibility of the Ising S = 1 model with biquadratic interactions is expanded in a high temperature series on the FCC lattice for a range of the BIC interaction parameter that includes the Potts model as discussed by the authors.
Abstract: The susceptibility of the Ising S=1 model with biquadratic interactions is expanded in a high temperature series on the FCC lattice for a range of the biquadratic interaction parameter that includes the Potts model (1952) A tricritical point and a point above which the magnetization M remains zero are approximately located The Potts model seems to fall in the region of the first-order phase transition in M
32 citations
TL;DR: In this paper, the Callan-Symanzik technique is applied to the continuous Potts model and it is shown that close to four dimensions the phase transition can be continuous if and only if the bare coupling of the cubic term, phi 13-3 phi 1 phi 22, vanishes, as predicted by the Landau criterion.
Abstract: The Callan-Symanzik technique is applied to the continuous Potts model. It is shown that close to four dimensions the phase transition can be continuous if and only if the bare coupling of the cubic term, phi 13-3 phi 1 phi 22, vanishes, as predicted by the Landau criterion. This is shown to be the result of the fact that the fixed point of the renormalized cubic coupling constant is at zero and is ultraviolet-stable.
27 citations
26 citations
TL;DR: In this article, the formalism for obtaining high-field expansions for the Potts model by means of partial generating functions is discussed, and the critical isotherm is investigated.
Abstract: The formalism for obtaining high-field expansions for the Potts model by means of partial generating functions is discussed. The critical isotherm is investigated.
19 citations
14 citations
TL;DR: In this paper, the two-spin correlation function of the Ising model on a Bethe lattice as a function of temperature and magnetic field was analyzed and it was shown that the coherence length is finite at finite temperatures.
TL;DR: In this paper, a formalism for series expansions and a new proof of the Kramers-Wannier symmetry on the square lattice are presented, and Pade approximants for the series expansions including a procedure explicitly utilizing the symmetry are discussed.
Abstract: Second-rank tensor order parameters appear for liquid crystals and crystallographic transitions. The simplest model with a disordered high-temperature state has interactions invariant under cubic spin transformations. It is shown that for spin 1 this leads to the 3-state Potts model. It is suggested that this model is therefore relevant to the understanding of phase transitions with such an order parameter. A formalism for series expansions and a new proof of the Kramers-Wannier symmetry on the square lattice are presented. Pade approximants for the series expansions including a procedure explicitly utilizing the symmetry are discussed. The negative interaction 'orthogonal' model analogous to the Ising antiferromagnet is also discussed and shown to have a highly degenerate ground state. On the square lattice this is the degeneracy of Lieb's ice. Relationships to ferroelectric models and the three-colour problem are also discussed.
TL;DR: In this paper, it was shown that if the free energy of the Ising model of spin 1/2 is expanded as a function of the magnetization and temperature, only star lattice constants enter in the expansion.
Abstract: It is shown by a direct method that if the free energy of the Ising model of spin 1/2 is expanded as a function of the magnetization and temperature, only star lattice constants enter in the expansion. It is deduced that the same property holds for the Potts model; there are indications that it also holds for the D spin classical vector models.
TL;DR: The interaction energy of the Potts model with 2 S + 1 states per site is of the form ∑ 〈 i,j 〉 δ S i S j where δ s i s j is the Kronecker delta symbol.
TL;DR: In this article, the low-temperature high-field polynomials for the free energy are given for the general Blume-Emery-Griffiths (1971) model on the FCC lattice.
Abstract: The low-temperature high-field polynomials for the free energy are given for the general Blume-Emery-Griffiths (1971) model on the FCC lattice. The order parameters and susceptibilities are obtained for three values of the biquadratic interaction and a specific form of the external field Delta . One of the treated cases is the Potts model.
TL;DR: The connection between the anisotropic Ising model and the second-neighbour is discussed in this article, and the results are consistent with the prediction that the Second Neighbour Ising Model on a simple quadratic lattice has critical behaviour described by scaling with respect to the nearest neighbor coupling strength.
Abstract: The connection between the anisotropic Ising model and the second-neighbour Ising model is discussed Series results are consistent with the prediction that the second-neighbour Ising model on a simple quadratic lattice has critical behaviour described by scaling with respect to the nearest-neighbour coupling strength
01 Jan 1974
TL;DR: In this paper, a brief review of some recent developments and open questions for Ising spin systems with ferromagnetic pair interactions are discussed, along with a discussion of open questions.
Abstract: We give a brief review of some recent developments and discuss some open questions for Ising spin systems with ferromagnetic pair interactions.