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

arXiv:0805.0711 · Physical Review E

Equilibriumlike extension of the invaded cluster algorithm

Ivan Balog, Katarina Uzelac

Published May 6, 2008• 3 citations
arXivHTMLPDF

Abstract

We propose an extension of the nonequilibrium invaded cluster (IC) algorithm, which reestablishes a correct scaling of fluctuations at criticality and also self-adjusts to the critical temperature. We show that by introducing a single constraint to the intrinsic quantity of the IC algorithm the temperature becomes well defined and the sampling of the equilibrium ensemble is regained. The procedure is applied to the Potts model in two and three dimensions.

DOI
10.1103/physreve.77.050101

Related papers

Equilibriumlike invaded cluster algorithm: Critical exponents and dynamical properties

Ivan Balog, Katarina Uzelac

We present a detailed study of the equilibrium-like invaded cluster algorithm, recently proposed as an extension of the invaded cluster algorithm, designed to drive the system to criticality while still preserving the equilibrium ensemble. We perform extensive simulations on two special cases of the Potts model and examine the precision of critical exponents by including the leading corrections. We show that both thermal and magnetic critical exponents can be obtained with high accuracy compared to the best available results. The choice of the auxiliary parameters of the algorithm is discussed in context of dynamical properties. We also discuss the relation to the Li-Sokal bound for the dynamical exponent z.

arXiv:1004.1509•Physical Review E•Apr 15, 2010•3 citations

Generalization of the invaded cluster algorithm to the tricritical point

Ivan Balog, Katarina Uzelac

The invaded cluster algorithm [1] is generalized [2] to the tricritical point on the example of 2d Potts model with annealed dilution. Self-regulating procedure that locates the tricritical point in the two-parameter space spanned by temperature and chemical potential of vacancies is constructed based on geometrical arguments. The tricritical point is identified as a simultaneous percolation of the Fortuin-Kastelyn cluster and the geometrical cluster consisting of vacancies and isolated spins. The tricritical values of parameters and concentration are presented for q=1, 2, 3 and found to be in a good agreement with the best known results [3]. Scaling properties of the percolating scaling cluster and related critical exponents are also derived. Based on the idea that effective correlation of vacancies is important at the tricritical point, we also examine alternative stopping rules within generalized IC algorithm, and possible extension to higher dimensions. [1] J. Machta, Y. S. Choi, A. Lucke, T. Schweizer, L. V. Chayes, Phys. Rev. Lett. 75, 2792 (1995) ; J. Machta, Y. S. Choi, A. Lucke, T. Schweizer, L. M. Chayes, Phys. Rev. E 54, 1332 (1996). [2] I. Balog, K.Uzelac, preprint cond-mat/0703759. [3] X. Qian, Y. Deng, H. W. J. Bl¨ote, Phys. Rev. E 72, 056132 (2005).

•Jan 1, 2007•0 citations

Invaded cluster algorithm for Potts models

Jonathan L. Machta, Yongsoo Choi, A. Lücke +2 more

The invaded cluster algorithm, a method for simulating phase transitions, is described in detail. Theoretical, albeit nonrigorous, justification of the method is presented and the algorithm is applied to Potts models in two and three dimensions. The algorithm is shown to be useful for both first-order and continuous transitions and evidently provides an efficient way to distinguish between these possibilities. The dynamic properties of the invaded cluster algorithm are studied. Numerical evidence suggests that the algorithm has no critical slowing for Ising models. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9605103•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Aug 1, 1996•80 citations

Dynamic and static properties of the invaded cluster algorithm

K. Moriarty, Jonathan L. Machta, L. Chayes

Simulations of the two-dimensional Ising and three-state Potts models at their critical points are performed using the invaded cluster (IC) algorithm. It is argued that observables measured on a sublattice of size l should exhibit a crossover to Swendsen-Wang (SW) behavior for l sufficiently less than the lattice size L, and a scaling form is proposed to describe the crossover phenomenon. It is found that the energy autocorrelation time ${\ensuremath{\tau}}_{\ensuremath{\varepsilon}}(l,L)$ for an $l\ifmmode\times\else\texttimes\fi{}l$ sublattice attains a maximum in the crossover region, and a dynamic exponent ${z}^{\mathrm{IC}}$ for the IC algorithm is defined according to ${\ensuremath{\tau}}_{\ensuremath{\varepsilon},\mathrm{max}}\ensuremath{\sim}{L}^{{z}^{\mathrm{IC}}}.$ Simulation results for the three-state model yield ${z}^{\mathrm{IC}}=0.346\ifmmode\pm\else\textpm\fi{}0.002,$ which is smaller than values of the dynamic exponent found for the SW and Wolff algorithms and also less than the Li-Sokal bound. The results are less conclusive for the Ising model, but it appears that ${z}^{\mathrm{IC}}<0.21$ and possibly that ${\ensuremath{\tau}}_{\ensuremath{\varepsilon},\mathrm{max}}\ensuremath{\sim}\mathrm{ln}L$ so that ${z}^{\mathrm{IC}}=0$---similar to previous results for the SW and Wolff algorithms.

arXiv:cond-mat/9811138•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Feb 1, 1999•8 citations

Probability-Changing Cluster Algorithm for Potts Models

Yusuke Tomita, Yutaka Okabe

We propose a new effective cluster algorithm of tuning the critical point automatically, which is an extended version of the Swendsen-Wang algorithm. We change the probability of connecting spins of the same type, p = 1-e(-J/k(B)T), in the process of the Monte Carlo spin update. Since we approach the canonical ensemble asymptotically, we can use the finite-size scaling analysis for physical quantities near the critical point. Simulating the two-dimensional Potts models to demonstrate the validity of the algorithm, we have obtained the critical temperatures and critical exponents which are consistent with the exact values; the comparison has been made with the invaded cluster algorithm.

arXiv:cond-mat/0011276•Physical Review Letters•Jan 22, 2001•56 citations

Invaded Cluster Algorithm for Equilibrium Critical Points

Jonathan L. Machta, Y. S. Choi, A. Lücke +2 more

A new cluster algorithm based on invasion percolation is described. The algorithm samples the critical point of a spin system without a priori knowledge of the critical temperature and provides an efficient way to determine the critical temperature and other observables in the critical region. The method is illustrated for the two- and three-dimensional Ising models. The algorithm equilibrates spin configurations much faster than the closely related Swendsen-Wang algorithm.

arXiv:cond-mat/9507094•Physical Review Letters•Oct 9, 1995•77 citations
We propose an extension of the nonequilibrium invaded cluster (IC) algorithm, which reestablishes a correct scaling of fluctuations at criticality and also self-adjusts to the critical temperature. We show that by introducing a single constraint to the intrinsic quantity of the IC algorithm the temperature becomes well defined and the sampling of the equilibrium ensemble is regained. The procedure is applied to the Potts model in two and three dimensions.
We present a detailed study of the equilibrium-like invaded cluster algorithm, recently proposed as an extension of the invaded cluster algorithm, designed to drive the system to criticality while still preserving the equilibrium ensemble. We perform extensive simulations on two special cases of the Potts model and examine the precision of critical exponents by including the leading corrections. We show that both thermal and magnetic critical exponents can be obtained with high accuracy compared to the best available results. The choice of the auxiliary parameters of the algorithm is discussed in context of dynamical properties. We also discuss the relation to the Li-Sokal bound for the dynamical exponent z.
The invaded cluster algorithm [1] is generalized [2] to the tricritical point on the example of 2d Potts model with annealed dilution. Self-regulating procedure that locates the tricritical point in the two-parameter space spanned by temperature and chemical potential of vacancies is constructed based on geometrical arguments. The tricritical point is identified as a simultaneous percolation of the Fortuin-Kastelyn cluster and the geometrical cluster consisting of vacancies and isolated spins. The tricritical values of parameters and concentration are presented for q=1, 2, 3 and found to be in a good agreement with the best known results [3]. Scaling properties of the percolating scaling cluster and related critical exponents are also derived. Based on the idea that effective correlation of vacancies is important at the tricritical point, we also examine alternative stopping rules within generalized IC algorithm, and possible extension to higher dimensions. [1] J. Machta, Y. S. Choi, A. Lucke, T. Schweizer, L. V. Chayes, Phys. Rev. Lett. 75, 2792 (1995) ; J. Machta, Y. S. Choi, A. Lucke, T. Schweizer, L. M. Chayes, Phys. Rev. E 54, 1332 (1996). [2] I. Balog, K.Uzelac, preprint cond-mat/0703759. [3] X. Qian, Y. Deng, H. W. J. Bl¨ote, Phys. Rev. E 72, 056132 (2005).
The invaded cluster algorithm, a method for simulating phase transitions, is described in detail. Theoretical, albeit nonrigorous, justification of the method is presented and the algorithm is applied to Potts models in two and three dimensions. The algorithm is shown to be useful for both first-order and continuous transitions and evidently provides an efficient way to distinguish between these possibilities. The dynamic properties of the invaded cluster algorithm are studied. Numerical evidence suggests that the algorithm has no critical slowing for Ising models. \textcopyright{} 1996 The American Physical Society.
Simulations of the two-dimensional Ising and three-state Potts models at their critical points are performed using the invaded cluster (IC) algorithm. It is argued that observables measured on a sublattice of size l should exhibit a crossover to Swendsen-Wang (SW) behavior for l sufficiently less than the lattice size L, and a scaling form is proposed to describe the crossover phenomenon. It is found that the energy autocorrelation time ${\ensuremath{\tau}}_{\ensuremath{\varepsilon}}(l,L)$ for an $l\ifmmode\times\else\texttimes\fi{}l$ sublattice attains a maximum in the crossover region, and a dynamic exponent zIC{z}^{\mathrm{IC}}zIC for the IC algorithm is defined according to ${\ensuremath{\tau}}_{\ensuremath{\varepsilon},\mathrm{max}}\ensuremath{\sim}{L}^{{z}^{\mathrm{IC}}}.$ Simulation results for the three-state model yield ${z}^{\mathrm{IC}}=0.346\ifmmode\pm\else\textpm\fi{}0.002,$ which is smaller than values of the dynamic exponent found for the SW and Wolff algorithms and also less than the Li-Sokal bound. The results are less conclusive for the Ising model, but it appears that zIC<0.21{z}^{\mathrm{IC}}<0.21zIC<0.21 and possibly that ${\ensuremath{\tau}}_{\ensuremath{\varepsilon},\mathrm{max}}\ensuremath{\sim}\mathrm{ln}L$ so that zIC=0{z}^{\mathrm{IC}}=0zIC=0---similar to previous results for the SW and Wolff algorithms.
We propose a new effective cluster algorithm of tuning the critical point automatically, which is an extended version of the Swendsen-Wang algorithm. We change the probability of connecting spins of the same type, p = 1-e(-J/k(B)T), in the process of the Monte Carlo spin update. Since we approach the canonical ensemble asymptotically, we can use the finite-size scaling analysis for physical quantities near the critical point. Simulating the two-dimensional Potts models to demonstrate the validity of the algorithm, we have obtained the critical temperatures and critical exponents which are consistent with the exact values; the comparison has been made with the invaded cluster algorithm.