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.

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

scholarly journals New Phase Transition Related to the Black Hole’s Topological Charge

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Shan-Quan Lan ◽  
Gu-Qiang Li ◽  
Jie-Xiong Mo ◽  
Xiao-Bao Xu
Keyword(s):  
Phase Transition ◽  
Specific Heat ◽  
Topological Charge ◽  
Energy Analysis ◽  
Van Der Waals ◽  
Tail Behavior ◽  
Maxwell Theory ◽  
Free Energy Analysis ◽  
Physical Quantities ◽  
New Phase

The topological charge ϵ of AdS black hole is introduced by Tian et al. in their papers, where a complete thermodynamic first law is obtained. In this paper, we investigate a new phase transition related to the topological charge in Einstein-Maxwell theory. Firstly, we derive the explicit solutions corresponding to the divergence of specific heat Cϵ and determine the phase transition critical point. Secondly, the T-r curve and T-S curve are investigated and they exhibit an interesting van der Waals system’s behavior. Critical physical quantities are also obtained which are consistent with those derived from the specific heat analysis. Thirdly, a van der Waals system’s swallow tail behavior is observed when ϵ>ϵc in the F-T graph. What is more, the analytic phase transition coexistence lines are obtained by using the Maxwell equal area law and free energy analysis, the results of which are consistent with each other.

KNOTTED VORTICES AND SUPERFLUID PHASE TRANSITION

1993 ◽  
Vol 07 (23) ◽  
pp. 1523-1526 ◽  
Author(s):  
ROBERT OWCZAREK
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Specific Heat ◽  
Superfluid Helium ◽  
Vortex Structures ◽  
Two Dimensional ◽  
Superfluid Phase ◽  
Λ Point

In this letter, studies of knotted vortex structures in superfluid helium are continued. A model of superfluid phase transition (λ-transition) is built in this framework. Similarities of this model to the two-dimensional Ising model are shown. Dependence of specific heat of superfluid helium on temperature near the λ point is explained.

THE STUDY OF QUENCHED BOND RANDOMNESS BY WANG–LANDAU ALGORITHM

2007 ◽  
Vol 18 (07) ◽  
pp. 1107-1117
Author(s):  
FATIH YAŞAR
Keyword(s):  
Phase Transition ◽  
Ground State ◽  
Probability Distributions ◽  
Spin Systems ◽  
State Entropy ◽  
First Order ◽  
First Order Phase Transition ◽  
Pure Case ◽  
First Order Phase ◽  
Physical Quantities

Monte Carlo simulations using the recently proposed Wang–Landau algorithm are performed to the q = 8 state Potts model in two dimension with various degrees of randomness. We systematically studied the effect of quenched bond randomness to system which has first-order phase transition. All simulations and measurements were done from pure case r = 1 to r = 0.4. Physical quantities such as energy density and ground-state entropy were evaluated at all temperatures. We have also obtained probability distributions of energy to monitor softening of transitions. It appears quite feasible to simulate spin systems with quenched bond randomness by Wang–Landau algorithm.

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.

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