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.

Concentration Phase Transition in a Two-Dimensional Ferromagnet

2020 ◽  
Vol 312 ◽  
pp. 244-250
Author(s):  
Alexander Konstantinovich Chepak ◽  
Leonid Lazarevich Afremov ◽  
Alexander Yuryevich Mironenko
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Thermal Effect ◽  
Spin State ◽  
Critical Concentration ◽  
Two Dimensional ◽  
Percolation Transition ◽  
Magnetic Cluster ◽  
The Monte Carlo Method

The concentration phase transition (CPT) in a two-dimensional ferromagnet was simulated by the Monte Carlo method. The description of the CPT was carried out using various order parameters (OP): magnetic, cluster, and percolation. For comparison with the problem of the geometric (percolation) phase transition, the thermal effect on the spin state was excluded, and thus, CPT was reduced to percolation transition. For each OP, the values ​​of the critical concentration and critical indices of the CPT are calculated.

The Investigation of Phase Transitions in Two-Dimensional 3-State Antiferromagnetic Potts Model on a Triangular Lattice with Interaction of Next Nearest Neighbors

2014 ◽  
Vol 215 ◽  
pp. 52-54 ◽  
Author(s):  
Akai K. Murtazaev ◽  
A.B. Babaev ◽  
Felix A. Kassan-Ogly
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Monte Carlo Method ◽  
Potts Model ◽  
Triangular Lattice ◽  
Exchange Interactions ◽  
Nearest Neighbors ◽  
Two Dimensional ◽  
Critical Temperatures ◽  
Antiferromagnetic Potts Model

The phase transitions and critical phenomena in two-dimensional 3-state antiferromagnetic Potts model with account of next-nearest neighbors are investigated by Monte-Carlo method. The systems with linear sizesL=20-144 are explored. Following parities of exchange interactions are considered. Moreover, we analyze the character of phase transitions and determine the critical temperatures.

Continuous phase transition in a disordered eight-states Potts model

2000 ◽  
Vol 13 (1) ◽  
pp. 107-110 ◽  
Author(s):  
F.W.S. Lima ◽  
J.E. Moreira ◽  
J.S. Andrade ◽  
U.M.S. Costa
Keyword(s):  
Phase Transition ◽  
Potts Model ◽  
Continuous Phase ◽  
Continuous Phase Transition

Computer simulation of the Potts model with the number of spin states q = 4 on a triangular lattice

2020 ◽  
pp. 57-64
Author(s):  
Magomedsheikh Ramazanov ◽  
Akai Murtazaev
Keyword(s):  
Computer Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Thermodynamic Properties ◽  
Potts Model ◽  
Triangular Lattice ◽  
Nearest Neighbors ◽  
Spin States ◽  
Two Dimensional ◽  
The Monte Carlo Method

Based on the Wang-Landau algorithm, the Monte Carlo method is used to study the thermodynamic properties of the two-dimensional Potts model with the number of spin states $q=4$ on a triangular lattice, taking into account the interactions of the first and second nearest neighbors. It is shown that taking into account antiferromagnetic interactions of the second nearest neighbors leads to frustration.

scholarly journals Phases of a matrix model with non-pairwise index contractions

2020 ◽  
Vol 2020 (7) ◽  
Author(s):  
Dennis Obster ◽  
Naoki Sasakura
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Matrix Model ◽  
Consistency Condition ◽  
Canonical Formalism ◽  
Continuous Phase ◽  
Spin Model ◽  
Tensor Model ◽  
Continuous Phase Transition

Abstract Recently a matrix model with non-pairwise index contractions has been studied in the context of the canonical tensor model, a tensor model for quantum gravity in the canonical formalism. This matrix model also appears in the same form with different ranges of parameters and variables, when the replica trick is applied to the spherical $p$-spin model ($p=3$) in spin glass theory. Previous studies of this matrix model suggested the presence of a continuous phase transition around $R\sim N^2/2$, where $N$ and $R$ designate its matrix size $N\times R$. This relation between $N$ and $R$ intriguingly agrees with a consistency condition of the tensor model in the leading order of $N$, suggesting that the tensor model is located near or on the continuous phase transition point and therefore its continuum limit is automatically taken in the $N\rightarrow \infty$ limit. In the previous work, however, the evidence for the phase transition was not satisfactory due to the slowdown of the Monte Carlo simulations. In this work, we provide a new setup for Monte Carlo simulations by integrating out the radial direction of the matrix. This new strategy considerably improves the efficiency, and allows us to clearly show the existence of the phase transition. We also present various characteristics of the phases, such as dynamically generated dimensions of configurations, cascade symmetry breaking and a parameter zero limit, and discuss their implications for the canonical tensor model.

scholarly journals Kinetic Models of Discrete Opinion Dynamics on Directed Barabási–Albert Networks

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 942 ◽  
Author(s):  
F. Welington S. Lima ◽  
J. A. Plascak
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Kinetic Models ◽  
Order Parameter ◽  
Majority Vote ◽  
Opinion Dynamics ◽  
Universality Class ◽  
Continuous Phase ◽  
Vote Model ◽  
Continuous Phase Transition

Kinetic models of discrete opinion dynamics are studied on directed Barabási–Albert networks by using extensive Monte Carlo simulations. A continuous phase transition has been found in this system. The critical values of the noise parameter are obtained for several values of the connectivity of these directed networks. In addition, the ratio of the critical exponents of the order parameter and the corresponding susceptibility to the correlation length have also been computed. It is noticed that the kinetic model and the majority-vote model on these directed Barabási–Albert networks are in the same universality class.

Structures and crystallization of vacuum-deposited amorphous Se and Sb films

1990 ◽  
Vol 48 (4) ◽  
pp. 140-141
Author(s):  
Makoto Shiojiri ◽  
Toshiyuki Isshiki ◽  
Tetsuya Fudaba ◽  
Yoshihiro Hirota
Keyword(s):  
Monte Carlo ◽  
Electron Microscope ◽  
Monte Carlo Method ◽  
Computer Program ◽  
Radial Distribution ◽  
Film Formation ◽  
Amorphous State ◽  
Two Dimensional ◽  
Amorphous Films ◽  
Binding Condition

In hexagonal Se crystal each atom is covalently bound to two others to form an endless spiral chain, and in Sb crystal each atom to three others to form an extended puckered sheet. Such chains and sheets may be regarded as one- and two- dimensional molecules, respectively. In this paper we investigate the structures in amorphous state of these elements and the crystallization.HRTEM and ED images of vacuum-deposited amorphous Se and Sb films were taken with a JEM-200CX electron microscope (Cs=1.2 mm). The structure models of amorphous films were constructed on a computer by Monte Carlo method. Generated atoms were subsequently deposited on a space of 2 nm×2 nm as they fulfiled the binding condition, to form a film 5 nm thick (Fig. 1a-1c). An improvement on a previous computer program has been made as to realize the actual film formation. Radial distribution fuction (RDF) curves, ED intensities and HRTEM images for the constructed structure models were calculated, and compared with the observed ones.

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