Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

TURKISH JOURNAL OF PHYSICS

Dynamics of Clusters in Three-Dimensional 3-State Potts Model

Fatih Yaşar, Y. Gündüç, Meral Aydın, Tarık Çelik

Published Jan 1, 1997• 0 citations
Publisher

Abstract

Dynamical evaluation of the observables changing per iteration in a Monte Carlo simulation possess vital information about the order of the phase transition occuring in the system ~[1]. Being a global operator, average cluster size is a good candidate to study the order of the phase transition. It is expected that study of cluster dynamics yields indicative information ~[1-3]. In this work cluster algorithm ~[4,5] is used to study the dynamical behavior of the average cluster size in $3$-dimensional 3-state Potts model ~[6] which is known to exhibit weak first-order transition ~[7]. Cluster size is calculated as the average of 1000 or higher replicas at each Monte Carlo iteration, during first few hundred iterations. Results for different sizes show the first-order character of the phase transition occuring in the model without performing time consuming computations to calculate the equilibrium averages.

DOI
10.55730/1300-0101.2453

Related papers

Study of Clusters in Two-Dimensional 7-State Potts Model

Burcu Ortakaya, Y. Gündüç, Meral Aydın +1 more

It is known that finite size scaling theory is well established for the systems undergoing a strong first-order transition [1-3]. However, if the correlation length is larger than the system size, methods using finite size scaling theory may fail to give indication of the first-order transition. The aim in this work is to observe how the system approaches to the first-order regime (where the correlation length is smaller but comparable to the size of the system) in two-dimensional 7-state Potts model which is known to exhibit first-order transition [4,5]. Cluster algorithm [6,7] is used to calculate commonly used equilibrium averages and the energy histogram, as well as cluster size related measurables like the average cluster size, fluctuations in the cluster size and the distribution of the cluster sizes [8,9]. The behavior of these measurables on different sizes varying from 8 \times 8 to 64 \times 64 is observed and the effect of this behavior on the order of the transition is studied.

TURKISH JOURNAL OF PHYSICS•Jan 1, 1997•0 citations

Cluster Study of Phase Transition in Two-Dimensional, q-State Potts Model

Meral Aydın, Y. Gündüç, Tarık Çelik +2 more

The two-dimensional $q$-state Potts model is studied through the variations in cluster size depending on temperature and the number of states $q$, using cluster algorithm. It is observed that cluster related measurables give evidence for the order of the transition at smaller lattice sizes than energy and during early iterations of the Monte Carlo simulation.

TURKISH JOURNAL OF PHYSICS•Jan 1, 1997•0 citations

A Numerical Study of the 2D Potts Model via the Cluster Algorithm

Meral Aydın, Tarık Çelik, Y. Gündüç

The two-dimensional q-state Potts model is studied with and without external field using a cluster algorithm. Equilibrium averages, fluctuations in the average cluster size and the histograms for energy, order parameter and the average cluster size are obtained as functions of the temperature. Studying the dynamical evolution of clusters through their size distributions and fluctuations provide helpful information on the order of phase transitions.

TURKISH JOURNAL OF PHYSICS•Jan 1, 1996•1 citation

Investigation of the critical behavior of the three-dimensional weakly diluted Potts model

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev, G. Ya. Aznaurova

The static critical behavior of the three-dimensional weakly diluted Potts model with the state q = 3 on a simple cubic lattice has been investigated by the Monte Carlo method using the Wolff single-cluster algorithm. It is shown that at the spin concentrations p = 0.9 and 0.8 a second-order phase transition is observed in the three-dimensional weakly diluted Potts model with the state q = 3. On the basis of the finite-size scaling theory, we calculated the static critical exponents of the specific heat α, susceptibility γ, magnetization β, and the correlation-length exponent v .

Bulletin of the Russian Academy of Sciences Physics•May 1, 2007•1 citation

Study of Cluster Distributions in Two-dimensional q-State Potts Model

Meral Aydın, Y. Gündüç, Tarık Çelik

Abstract The two-dimensional Potts Model with 2 to 10 states is studied using a cluster algorithm to calculate fluctuations in cluster size, distributions of cluster sizes as well as commonly used quantities like equilibrium averages and the histograms for energy and the order parameter. Results provide information about the variation of cluster sizes depending on the temperature and the number of states. They also give evidence for first-order transition when energy and the order parameter related measurables are inconclusive on small size lattices.

arXiv:hep-lat/9601018•Jan 26, 1996•0 citations

Investigation of Phase Transitions in the Site-Diluted Three-Dimensional Potts Model

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev

The phase transitions and critical phenomena in three-dimensional (3D) site-diluted 3-and 4-state Potts models is investigated by Monte-Carlo method based on the highly efficient Wolff algorithm. The systems with linear sizesL=20-44 at spin concentrationsp=1.00, 0.95, 0.90, 0.80, 0.70, 0.65 are explored. The second-order phase transition is shown to occur in the three-dimensional 3-state Potts model with nonmagnetic impurities. In the 4-state Potts model there are observed first-order phase transitions in weakly diluted state, when the model is strongly diluted the first-order phase transitions change to the second-order one. On the basis of the finite-size scaling theory static critical exponents of specific heatα, susceptibilityγ, magnetizationβ, and exponent of correlation radiusνfor the systems under study are calculated.

Diffusion and defect data, solid state data. Part B, Solid state phenomena/Solid state phenomena•Jun 1, 2012•0 citations
Dynamical evaluation of the observables changing per iteration in a Monte Carlo simulation possess vital information about the order of the phase transition occuring in the system ~[1]. Being a global operator, average cluster size is a good candidate to study the order of the phase transition. It is expected that study of cluster dynamics yields indicative information ~[1-3]. In this work cluster algorithm ~[4,5] is used to study the dynamical behavior of the average cluster size in 333-dimensional 3-state Potts model ~[6] which is known to exhibit weak first-order transition ~[7]. Cluster size is calculated as the average of 1000 or higher replicas at each Monte Carlo iteration, during first few hundred iterations. Results for different sizes show the first-order character of the phase transition occuring in the model without performing time consuming computations to calculate the equilibrium averages.
It is known that finite size scaling theory is well established for the systems undergoing a strong first-order transition [1-3]. However, if the correlation length is larger than the system size, methods using finite size scaling theory may fail to give indication of the first-order transition. The aim in this work is to observe how the system approaches to the first-order regime (where the correlation length is smaller but comparable to the size of the system) in two-dimensional 7-state Potts model which is known to exhibit first-order transition [4,5]. Cluster algorithm [6,7] is used to calculate commonly used equilibrium averages and the energy histogram, as well as cluster size related measurables like the average cluster size, fluctuations in the cluster size and the distribution of the cluster sizes [8,9]. The behavior of these measurables on different sizes varying from 8 \times 8 to 64 \times 64 is observed and the effect of this behavior on the order of the transition is studied.
The two-dimensional qqq-state Potts model is studied through the variations in cluster size depending on temperature and the number of states qqq, using cluster algorithm. It is observed that cluster related measurables give evidence for the order of the transition at smaller lattice sizes than energy and during early iterations of the Monte Carlo simulation.
The static critical behavior of the three-dimensional weakly diluted Potts model with the state q = 3 on a simple cubic lattice has been investigated by the Monte Carlo method using the Wolff single-cluster algorithm. It is shown that at the spin concentrations p = 0.9 and 0.8 a second-order phase transition is observed in the three-dimensional weakly diluted Potts model with the state q = 3. On the basis of the finite-size scaling theory, we calculated the static critical exponents of the specific heat α, susceptibility γ, magnetization β, and the correlation-length exponent v .
Abstract The two-dimensional Potts Model with 2 to 10 states is studied using a cluster algorithm to calculate fluctuations in cluster size, distributions of cluster sizes as well as commonly used quantities like equilibrium averages and the histograms for energy and the order parameter. Results provide information about the variation of cluster sizes depending on the temperature and the number of states. They also give evidence for first-order transition when energy and the order parameter related measurables are inconclusive on small size lattices.
The phase transitions and critical phenomena in three-dimensional (3D) site-diluted 3-and 4-state Potts models is investigated by Monte-Carlo method based on the highly efficient Wolff algorithm. The systems with linear sizesL=20-44 at spin concentrationsp=1.00, 0.95, 0.90, 0.80, 0.70, 0.65 are explored. The second-order phase transition is shown to occur in the three-dimensional 3-state Potts model with nonmagnetic impurities. In the 4-state Potts model there are observed first-order phase transitions in weakly diluted state, when the model is strongly diluted the first-order phase transitions change to the second-order one. On the basis of the finite-size scaling theory static critical exponents of specific heatα, susceptibilityγ, magnetizationβ, and exponent of correlation radiusνfor the systems under study are calculated.