Interface properties of the three-state potts model in two dimensions

1982 ◽  
Vol 47 (4) ◽  
pp. 335-340 ◽  
Author(s):  
Walter Selke ◽  
Werner Pesch
Keyword(s):  
Potts Model ◽  
Two Dimensions ◽  
Interface Properties

Phase transitions in the six‐state vector Potts model in two dimensions

1984 ◽  
Vol 55 (6) ◽  
pp. 2429-2431 ◽  
Author(s):  
Challa S. S. Murty ◽  
D. P. Landau
Keyword(s):  
Phase Transitions ◽  
Potts Model ◽  
State Vector ◽  
Two Dimensions

SURFACE CRITICAL BEHAVIOUR OF SOME TWO-DIMENSIONAL LATTICE MODELS

1990 ◽  
Vol 04 (09) ◽  
pp. 1437-1464 ◽  
Author(s):  
A.L. STELLA ◽  
C. VANDERZANDE
Keyword(s):  
Potts Model ◽  
Conformal Invariance ◽  
Finite Size ◽  
Lattice Models ◽  
Universality Class ◽  
Two Dimensions ◽  
Point Of View ◽  
Critical Behaviour ◽  
Logarithmic Scaling ◽  
Theta Point

A review is given of recent work on the ordinary surface critical behaviour of systems in two dimensions. Several models of interest in statistical mechanics are considered: Potts model, percolation, Ising clusters, ZN-model, O(n) model and polymers. Numerical results for surface exponents, obtained by suitable finite size scaling extrapolations, are discussed in the light of recent advances based on the conformal invariance approach. Surface exponents are often seen as important tests of conformal invariance predictions. In other cases these exponents provide important information for a location of the problem within the classification schemes offered by the conformal approach, and a determination of its universality class. A relevant example of the first aspect is the study of the q-state Potts model with q near 4, for which an analytical study of logarithmic scaling corrections is needed to achieve a successful test. The latter point of view applies, e.g., to the more controversial cases of polymers at the theta point and critical Ising clusters. Emphasis is put on the importance of an integrated study of both bulk and surface properties. Relevant issues, like the possible existence of analytical expressions for the indices in particular model families, or of general relationships between bulk and surface exponents, are critically discussed. The new problem of critical behaviour at fractal boundaries is also considered for random (RW) and self-avoiding walks (SAW). From the numerical analysis of this problem remarkable universalities of the surface exponents seem to emerge, which, in the case of SAW’s, are still far from being understood.

Exact results for the Potts model in two dimensions

1978 ◽  
Vol 19 (6) ◽  
pp. 623-632 ◽  
Author(s):  
A. Hintermann ◽  
H. Kunz ◽  
F. Y. Wu
Keyword(s):  
Potts Model ◽  
Two Dimensions ◽  
Exact Results

SOFTENING OF PHASE TRANSITION BY RANDOM DISTRIBUTION OF BIMODAL-BONDS IN THE 2D 8-STATE POTTS MODEL

1999 ◽  
Vol 10 (05) ◽  
pp. 961-966
Author(s):  
FATIH YAŞAR ◽  
YIĞIT GÜNDÜÇ ◽  
TARIK ÇELIK
Keyword(s):  
Phase Transition ◽  
Potts Model ◽  
Random Distribution ◽  
Finite Size ◽  
Threshold Value ◽  
Two Dimensions ◽  
First Order ◽  
Size Dependent ◽  
First Order Phase Transition ◽  
First Order Phase

We investigated the influence of the distribution of bimodal bonds on phase transition in 8-state Potts model in two dimensions. We show that there is a finite size dependent threshold value of the introduced quenched randomness in the bond distribution for rounding the first-order phase transition.

Dilute Potts model in two dimensions

2005 ◽  
Vol 72 (5) ◽  
Author(s):  
Xiaofeng Qian ◽  
Youjin Deng ◽  
Henk W. J. Blöte
Keyword(s):  
Potts Model ◽  
Two Dimensions
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