scholarly journals TheXY model and the three-state antiferromagnetic Potts model in three dimensions: Critical properties from fluctuating boundary conditions

1994 ◽  
Vol 77 (3-4) ◽  
pp. 919-930 ◽  
Author(s):  
Aloysius P. Gottlob ◽  
Martin Hasenbusch
Keyword(s):  
Boundary Conditions ◽  
Potts Model ◽  
Three Dimensions ◽  
Critical Properties ◽  
Antiferromagnetic Potts Model

FINITE TEMPERATURE ENTROPY OF THE ANTIFERROMAGNETIC POTTS MODEL

1988 ◽  
Vol 02 (06) ◽  
pp. 1495-1501 ◽  
Author(s):  
X. Y. CHEN ◽  
C. Y. PAN
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Potts Model ◽  
Finite Temperature ◽  
Three Dimensions ◽  
Universal Relation ◽  
Zero Temperature ◽  
Disorder Transition ◽  
Color Problem ◽  
Antiferromagnetic Potts Model

Monte Carlo simulation is used to deal with the finite temperature entropy of the q-state antiferromagnetic Potts model which is the extension of the general q-color problem (at zero temperature). The finite temperature entropy of the model in two and three dimensions is obtained which is consistent with the zero temperature results. A possible universal relation of the model to determine when the order-disorder transition happens is proposed.

scholarly journals Critical properties of 2d disordered 3-state antiferromagnetic potts model ON TRIANGULAR LATTICE

2018 ◽  
Vol 185 ◽  
pp. 11001
Author(s):  
A.K. Murtazaev ◽  
A.B. Babaev ◽  
G.Y. Ataeva
Keyword(s):  
Potts Model ◽  
Triangular Lattice ◽  
Finite Size ◽  
Correlation Radius ◽  
Magnetic Impurities ◽  
Critical Properties ◽  
First Order ◽  
Wolff Algorithm ◽  
Antiferromagnetic Potts Model ◽  
Single Cluster

By introducing a small amount of non-magnetic impurities into an antiferromagnetic (AF) two-dimensional (2D) Potts model on a triangular lattice it is that the impurities in spin systems described by this model result in the change of a first order to a second-order phase transition. The systems with linear sizes L × L = N, L = 9-144 are considered. Investigations are performed using the standard Metropolis algorithm along with Monte-Carlo single-cluster Wolff algorithm. On the basis of the theory of finite-size scaling, critical exponents (CE) are calculated: the heat capacity α, the susceptibility γ, the order parameter β, and the CE of the correlation radius ν.

scholarly journals Integrable boundary conditions in the antiferromagnetic Potts model

2020 ◽  
Vol 2020 (5) ◽  
Author(s):  
Niall F. Robertson ◽  
Michal Pawelkiewicz ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Boundary Conditions ◽  
Potts Model ◽  
Antiferromagnetic Potts Model ◽  
Integrable Boundary Conditions

Solution of Navier’s Equation in Cylindrical Curvilinear Coordinates

1978 ◽  
Vol 45 (4) ◽  
pp. 812-816 ◽  
Author(s):  
B. S. Berger ◽  
B. Alabi
Keyword(s):  
Fourier Transform ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Half Space ◽  
Coordinate Transformation ◽  
Numerical Results ◽  
Three Dimensions ◽  
Curvilinear Coordinates ◽  
Rectangular Region

A solution has been derived for the Navier equations in orthogonal cylindrical curvilinear coordinates in which the axial variable, X3, is suppressed through a Fourier transform. The necessary coordinate transformation may be found either analytically or numerically for given geometries. The finite-difference forms of the mapped Navier equations and boundary conditions are solved in a rectangular region in the curvilinear coordinaties. Numerical results are given for the half space with various surface shapes and boundary conditions in two and three dimensions.

scholarly journals Uniqueness for the 3-state antiferromagnetic Potts model on the tree

2018 ◽  
Vol 23 (0) ◽  
Author(s):  
Andreas Galanis ◽  
Leslie Ann Goldberg ◽  
Kuan Yang
Keyword(s):  
Potts Model ◽  
Antiferromagnetic Potts Model
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