MULTICOMPONENT CHIRAL POTTS MODELS

1992 ◽  
Vol 07 (supp01b) ◽  
pp. 1007-1023 ◽  
Author(s):  
HELEN AU-YANG ◽  
JACQUES H. H. PERK
Keyword(s):  
Potts Model ◽  
Lattice Site ◽  
Nearest Neighbor ◽  
Composite Model ◽  
Dual Lattice ◽  
Chiral Potts Model ◽  
Potts Models ◽  
Spin Interactions ◽  
Composite Models ◽  
Relative Prime

It is shown that an (Nρ,Nσ) chiral Potts model, which is a generalization of the Ashkin-Teller model and consists of two chiral Potts models which are coupled together by four-spin interactions, can always be mapped to a single chiral Potts model of NρNσ states if Nρ and Nσ are relative prime. Moreover, if on every lattice site there are d spins with Nρ,…,Nσ states, respectively, similar mappings exist: If there are chiral two-spin interactions between nearest neighbor spins of the same kind and if the d sublattices are coupled together by chiral 2j-spin interactions for j≤d between the j pairs of spins, this defines a composite (Nρ,…,Nσ) state chiral Potts model. If (Ni,Nj)=1, for i≠j, i,j=1,…,d, then the composite model with (Nρ,…,Nσ) states can be mapped into a [Formula: see text]-state chiral Potts model. Finally, it is shown that if one or more of the spins of a unit cell sits on the dual lattice whereas the other spins sit on the original lattice, so that this is a generalization of the eight-vertex model in the spin language, such a mapping also exists. This mean that results obtained for the chiral Potts models can be used for many such composite models.

scholarly journals DEFORMATIONS OF DYNAMICS ASSOCIATED TO THE CHIRAL POTTS MODEL

1992 ◽  
Vol 06 (22) ◽  
pp. 3575-3584 ◽  
Author(s):  
M.P. BELLON ◽  
J-M. MAILLARD ◽  
G. ROLLET ◽  
C-M. VIALLET
Keyword(s):  
Finite Order ◽  
Potts Model ◽  
Discrete Groups ◽  
Chiral Potts Model ◽  
Potts Models ◽  
Deformation Parameters ◽  
Fermat Number ◽  
Non Linear ◽  
The Stability

We describe deformations of non-linear (birational) representations of discrete groups generated by involutions, having their origin in the theory of the symmetric five-state Potts model. One of the deformation parameters can be seen as the number q of states of a chiral Potts models. This analogy becomes exact when q is a Fermat number. We analyze the stability of the corresponding dynamics, with a particular attention to orbits of finite order.

scholarly journals ON INHOMOGENEOUS p-ADIC POTTS MODEL ON A CAYLEY TREE

2005 ◽  
Vol 08 (02) ◽  
pp. 277-290 ◽  
Author(s):  
FARRUKH MUKHAMEDOV ◽  
UTKIR ROZIKOV
Keyword(s):  
Gibbs Measure ◽  
Potts Model ◽  
Cayley Tree ◽  
Nearest Neighbor ◽  
Gibbs Measures ◽  
Nearest Neighbors ◽  
Translation Invariant

We consider a nearest-neighbor inhomogeneous p-adic Potts (with q≥2 spin values) model on the Cayley tree of order k≥1. The inhomogeneity means that the interaction Jxy couplings depend on nearest-neighbors points x, y of the Cayley tree. We study (p-adic) Gibbs measures of the model. We show that (i) if q∉pℕ then there is unique Gibbs measure for any k≥1 and ∀ Jxy with | Jxy |< p-1/(p -1). (ii) For q∈p ℕ, p≥3 one can choose Jxy and k≥1 such that there exist at least two Gibbs measures which are translation-invariant.

scholarly journals QUASI-PARTICLES IN THE CHIRAL POTTS MODEL

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3601-3621 ◽  
Author(s):  
RINAT KEDEM ◽  
BARRY M. McCOY
Keyword(s):  
Transfer Matrix ◽  
Potts Model ◽  
Numerical Study ◽  
Particle Spectrum ◽  
Exact Results ◽  
Chiral Potts Model ◽  
Quasi Particle ◽  
Massive Phase ◽  
Matrix Eigenvalues ◽  
Potts Chain

We study the quasi-particle spectrum of the integrable three-state chiral Potts chain in the massive phase by combining a numerical study of the zeros of associated transfer matrix eigenvalues with the exact results of the ferromagnetic three-state Potts chain and the three-state superintegrable chiral Potts model. We find that the spectrum is described in terms of quasi-particles with momenta restricted only to segments of the Brillouin zone 0≤P≤2π where the boundaries of the segments depend on the chiral angles of the model.

A Monte Carlo and renormalization group study of the Ising model with nearest and next nearest neighbor interactions on the triangular lattice

1983 ◽  
Vol 61 (11) ◽  
pp. 1515-1527 ◽  
Author(s):  
James Glosli ◽  
Michael Plischke
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Ising Model ◽  
Potts Model ◽  
Triangular Lattice ◽  
Nearest Neighbor ◽  
Universality Class ◽  
Energy Functional ◽  
First Order ◽  
Universality Classes

The Ising model with nearest and next nearest neighbor antiferromagnetic interactions on the triangular lattice displays, for Jnnn/Jnn = 0.1, three phase transitions in different universality classes as the magnetic field is increased. We have studied this model using Monte Carlo and renormalization group techniques. The transition from the paramagnetic to the 2 × 1 phase (universality class of the Heisenberg model with cubic anisotropy) is found to be first order; the transition from the paramagnetic phase to the [Formula: see text] phase (universality class of the three state Potts model) is continuous; and the transition from the paramagnetic to the 2 × 2 phase (universality class of the four state Potts model) is found to change from first order to continuous as the field is increased. We have mapped out the phase diagram and determined the critical exponents for the continuous transitions. A novel technique, using a Landau-like free energy functional determined from Monte Carlo calculations, to distinguish between first order and continuous transitions, is described.

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