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

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

Burcu Ortakaya, Y. Gündüç, Meral Aydın, Tarık Çelik

Published Jan 1, 1997• 0 citations
Publisher

Abstract

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.

DOI
10.55730/1300-0101.2452

Related papers

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

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

Fatih Yaşar, Y. Gündüç, Meral Aydın +1 more

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.

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

Monte Carlo study of finite-size effects at a weakly first-order phase transition

Pawel Peczak, D. P. Landau

A new kind of finite-size phenomenon in the five-state Potts model in two dimensions, a ``false'' ground state, was recently reported by Katznelson and Lauwers based on Monte Carlo studies of large lattices. We reexamine the behavior of this weakly first-order system by performing extensive Monte Carlo simulations, and demonstrate that the ``novel'' states previously observed in internal-energy-distribution histograms tend to disappear when runs of sufficient length are used. We present evidence that very strong critical slowing down and a pseudodivergent correlation length are responsible for the observed effects. Our additional analysis of finite-size effects in the ten-state Potts model on small lattices (L\ensuremath{\le}10) shows a crossover of scaling from ${L}^{\mathrm{\ensuremath{-}}d}$ behavior (observed earlier on larger lattices) to a nonanalytic form. This result is used to discuss the observed nonanalytic scaling of thermodynamic quantities in the five-state Potts model.

Physical review. B, Condensed matter•Jun 1, 1989•95 citations

Cluster Study in the Three-Dimensional 3-State Potts Model

M. Aydin, T. Çelik, Y. Gündüç

The three-dimensional 3-state Potts model has been investigated by examining the average cluster size distributions. Cluster distributions give evidence for the weak first-order nature of the transition for lattice sizes as small as 163, where the energy histogram method fails to exhibit the true nature of the transition.

International Journal of Modern Physics C•Oct 1, 1997•2 citations

Phase transitions in the two-dimensional ferro- and antiferromagnetic potts models on a triangular lattice

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev

The phase transitions in the two-dimensional ferro- and antiferromagnetic Potts models with q = 3 states of spin on a triangular lattice are studied using cluster algorithms and the classical Monte Carlo method. Systems with linear sizes L = 20–120 are considered. The method of fourth-order Binder cumulants and histogram analysis are used to discover that a second-order phase transition occurs in the ferromagnetic Potts model and a first-order phase transition takes place in the antiferromagnetic Potts model. The static critical indices of heat capacity (α), magnetic susceptibility (γ), magnetization (β), and correlation radius index (ν) are calculated for the ferromagnetic Potts model using the finite-size scaling theory.

Journal of Experimental and Theoretical Physics•Dec 1, 2012•17 citations
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.
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.
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.
A new kind of finite-size phenomenon in the five-state Potts model in two dimensions, a ``false'' ground state, was recently reported by Katznelson and Lauwers based on Monte Carlo studies of large lattices. We reexamine the behavior of this weakly first-order system by performing extensive Monte Carlo simulations, and demonstrate that the ``novel'' states previously observed in internal-energy-distribution histograms tend to disappear when runs of sufficient length are used. We present evidence that very strong critical slowing down and a pseudodivergent correlation length are responsible for the observed effects. Our additional analysis of finite-size effects in the ten-state Potts model on small lattices (L\ensuremath{\le}10) shows a crossover of scaling from ${L}^{\mathrm{\ensuremath{-}}d}$ behavior (observed earlier on larger lattices) to a nonanalytic form. This result is used to discuss the observed nonanalytic scaling of thermodynamic quantities in the five-state Potts model.
The phase transitions in the two-dimensional ferro- and antiferromagnetic Potts models with q = 3 states of spin on a triangular lattice are studied using cluster algorithms and the classical Monte Carlo method. Systems with linear sizes L = 20–120 are considered. The method of fourth-order Binder cumulants and histogram analysis are used to discover that a second-order phase transition occurs in the ferromagnetic Potts model and a first-order phase transition takes place in the antiferromagnetic Potts model. The static critical indices of heat capacity (α), magnetic susceptibility (γ), magnetization (β), and correlation radius index (ν) are calculated for the ferromagnetic Potts model using the finite-size scaling theory.