Phase transition of a two-dimensional, multiplicatively coupledXY–Potts model

2009 ◽  
Vol 42 (22) ◽  
pp. 225001 ◽  
Author(s):  
Marcel Hellmann ◽  
Youjin Deng ◽  
Matthias Weiss ◽  
Dieter W Heermann
Keyword(s):  
Phase Transition ◽  
Potts Model ◽  
Two Dimensional

Phase Transition Temperature of Ferroelectric Thin Film Evaluated by Four-State Potts Model

2005 ◽  
Vol 902 ◽  
Author(s):  
Wing Yee Winnie Chung ◽  
Veng Cheong Lo
Keyword(s):  
Thin Film ◽  
Phase Transition ◽  
Boundary Condition ◽  
Transition Temperature ◽  
Potts Model ◽  
Domain Walls ◽  
Ferroelectric Thin Film ◽  
Two Dimensional ◽  
Thermally Activated ◽  
Phase Transition Temperatures

AbstractAn epitaxial ferroelectric thin film can be modeled by a two-dimensional array of dipoles. The orientation of each dipole is assigned to one of the four possible states which are mutually perpendicular to each other. Consequently, the whole film can be divided into domains with both 90° and 180° domain walls. The dominant switching mechanism for individual dipole is implemented by a 90° rotation. Two different conditions have been considered. For the first one (model A), every dipole inside the film is allowed to rotate, provided that it is thermally activated. For the second (model B), only the dipole rotation is restricted to those at the domain walls. The phase transition temperatures under these two models have been evaluated. Furthermore, the effects of sample size and boundary condition are discussed.

scholarly journals Фазовые переходы в двумерной слабо разбавленной пятивершинной модели Поттса

2020 ◽  
Vol 62 (7) ◽  
pp. 1088
Author(s):  
А.К. Муртазаев ◽  
А.Б. Бабаев ◽  
Г.Я. Атаева
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Potts Model ◽  
Square Lattice ◽  
Study Phase ◽  
Two Dimensional ◽  
Nonmagnetic Impurities ◽  
First Order Phase Transition ◽  
First Order Phase ◽  
Binder Cumulants

Computer simulation was used to study phase transitions in the two-dimensional weakly diluted Potts model on a square lattice at q=5. Systems with linear dimensions L×L=N, L=10-120 are considered. Based on fourth-order Binder cumulants, it was shown that the introduction of nonmagnetic impurities into the spin system described by the two-dimensional Potts model with q=5 leads to a change in the first-order phase transition to the second-order phase transition.

IMPORTANCE-SAMPLING MONTE CARLO METHOD AND ENTROPY OF q-STATE POTTS MODEL

1992 ◽  
Vol 06 (18) ◽  
pp. 1121-1129
Author(s):  
HSING-MEI HUANG
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Importance Sampling ◽  
Potts Model ◽  
Continuous Phase ◽  
Entropy Function ◽  
Two Dimensional ◽  
Potts Models ◽  
Continuous Phase Transition

An importance-sampling Monte Carlo method is applied to the calculation of Γ(E), the number of states for a given energy E, and Γ(E, S), the number of states for given energy E and spin S, of antiferromagnetic two-dimensional q=2,3,4,5,6 Potts models. The entropy function is derived for various temperatures, and our results for the q=3 model show a continuous phase transition.

DENSITY-OF-STATES MONTE CARLO METHOD FOR SIMULATION OF TWO-DIMENSIONAL RANDOM BOND POTTS MODEL

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2745-2751
Author(s):  
YOU YU ◽  
HE-PING YING ◽  
QING-HU CHEN ◽  
ZHENG-QUAN PAN
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Thermodynamic Properties ◽  
Density Of States ◽  
Potts Model ◽  
Bimodal Distribution ◽  
The Self ◽  
Two Dimensional ◽  
Finite Lattices

Softening of the phase transition and critical phenomena for the 2D random-bond Potts ferromagnet is investigated by using the density-of-states Monte Carlo method to calculate the thermodynamic properties with a variety of the quenched bond-randomness characterized by a disorder amplitude r=Ks/Kw. The numerical results show that the crossover from the 1st- to 2nd-order transition was induced at finite lattices for the self-dual bimodal distribution.

scholarly journals Softening of the phase transition in a two-dimensional Potts model under quenched bond randomness

1998 ◽  
Vol 58 (4) ◽  
pp. 4210-4212 ◽  
Author(s):  
Fatih Yaşar ◽  
Yiğit Gündüç ◽  
Tarık Çelik
Keyword(s):  
Phase Transition ◽  
Potts Model ◽  
Two Dimensional

MULTICANONICAL SIMULATION OF THE TWO-DIMENSIONAL 7-STATE POTTS MODEL

1992 ◽  
Vol 03 (05) ◽  
pp. 1137-1146 ◽  
Author(s):  
WOLFHARD JANKE
Keyword(s):  
Phase Transition ◽  
Potts Model ◽  
Lattice Gauge Theory ◽  
Two Dimensional ◽  
First Order ◽  
Lattice Gauge ◽  
Disordered Phase ◽  
First Order Phase Transition ◽  
Order Of Magnitude ◽  
First Order Phase

Using multicanonical Monte Carlo simulations, we have calculated the interface free energy between the coexisting ordered and disordered phase at the temperature driven first-order phase transition of the two-dimensional 7-state Potts model. Our result 2f3= 0.0241±0.0010 is about an order of magnitude smaller than other estimates in the recent literature. We discuss the differences in analysis and give a possible explanation for the discrepancy. Finally, we briefly mention similar investigations at the deconfining phase transition of SU(3) lattice gauge theory.

THE STUDY OF PHASE TRANSITION BY PERIODIC DISTRIBUTION OF BIMODAL BONDS IN 2D POTTS MODEL

2009 ◽  
Vol 20 (02) ◽  
pp. 223-236
Author(s):  
FATIH YAŞAR ◽  
MEHMET DILAVER
Keyword(s):  
Phase Transition ◽  
Specific Heat ◽  
Potts Model ◽  
Probability Distributions ◽  
Point Of View ◽  
Single Peak ◽  
Simulation Methods ◽  
Two Dimensional ◽  
Periodic Distribution ◽  
Physical Quantities

We have studied the influence of the distribution of bimodal bonds on the phase transition in two-dimensional 8-state Potts model by the recently proposed Wang–Landau (WL) and the Swendsen–Wang (SW) algorithm. All simulations and measurements are done for r = 0.5. Physical quantities such as energy density and specific heat are evaluated at all temperatures. We have also obtained the probability distributions of the energy in order to monitor the transitions. We have observed that some cases of the periodically arranged bond distributions show a single peak, and some cases show double or triple peaks in the specific heat. Besides, it seems that the appearing of these peaks in the specific heat relates to a blocking procedure for periodicity. When the number of interaction pairs between the bimodal bonds is increased on the lattice with the blocking procedure, one can observe a single peak, otherwise, one can observe a double or triple peaks in the specific heat. From the point of view of simulation methods, the WL algorithm also works efficiently in the simulation of the system for a periodically arranged bond distribution as well as the SW algorithm.

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