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:cond-mat/0502035 · Europhysics Letters (EPL)

Disorder-driven phase transitions of the large q -state Potts model in three dimensions

Maria Teresa Mercaldo, J C Anglès d'Auriac, Ferenc Iglói

Published May 17, 2005• 19 citations
arXivHTMLPDF

Abstract

Phase transitions induced by varying the strength of disorder in the large- q state Potts model in 3d are studied by analytical and numerical methods. By switching on the disorder, the transition stays of first order, but different thermodynamical quantities display essential singularities. Only for strong enough disorder will the transition be soften into a second-order one, in which case the ordered phase becomes non-homogeneous at large scales, while the non-correlated sites percolate the sample. In the critical regime the critical exponents are found universal: β/ν = 0.60(2) and ν = 0.73(1).

DOI
10.1209/epl/i2005-10042-2

Related papers

Critical and tricritical singularities of the three-dimensional random-bond Potts model for large q

Maria Teresa Mercaldo, J C Anglès d'Auriac, Ferenc Iglói

We study the effect of varying strength $\ensuremath{\delta}$ of bond randomness on the phase transition of the three-dimensional Potts model for large $q$. The cooperative behavior of the system is determined by large correlated domains in which the spins point in the same direction. These domains have a finite extent in the disordered phase. In the ordered phase there is a percolating cluster of correlated spins. For a sufficiently large disorder $\ensuremath{\delta}>{\ensuremath{\delta}}_{t}$ this percolating cluster coexists with a percolating cluster of noncorrelated spins. Such a coexistence is only possible in more than two dimensions. We argue and check numerically that ${\ensuremath{\delta}}_{t}$ is the tricritical disorder, which separates the first- and second-order transition regimes. The tricritical exponents are estimated as ${\ensuremath{\beta}}_{t}∕{\ensuremath{\nu}}_{t}=0.10(2)$ and ${\ensuremath{\nu}}_{t}=0.67(4)$. We claim these exponents are $q$ independent for sufficiently large $q$. In the second-order transition regime the critical exponents ${\ensuremath{\beta}}_{t}∕{\ensuremath{\nu}}_{t}=0.60(2)$ and ${\ensuremath{\nu}}_{t}=0.73(1)$ are independent of the strength of disorder.

arXiv:cond-mat/0511203•Physical Review E•Feb 23, 2006•21 citations

Disorder-induced rounding of the phase transition in the large- q -state Potts model

Maria Teresa Mercaldo, J C Anglès d'Auriac, Ferenc Iglói

The phase transition in the q -state Potts model with homogeneous ferromagnetic couplings is strongly first order for large q, while it is rounded in the presence of quenched disorder. Here we study this phenomenon on different two-dimensional lattices by using the fact that the partition function of the model is dominated by a single diagram of the high-temperature expansion, which is calculated by an efficient combinatorial optimization algorithm. For a given finite sample with discrete randomness the free energy is a piecewise linear function of the temperature, which is rounded after averaging, however, the discontinuity of the internal energy at the transition point (i.e., the latent heat) stays finite even in the thermodynamic limit. For a continuous disorder, instead, the latent heat vanishes. At the phase transition point the dominant diagram percolates and the total magnetic moment is related to the size of the percolating cluster. Its fractal dimension is found d(f) = ( 5 + square root of 5)/4 and it is independent of the type of the lattice and the form of disorder. We argue that the critical behavior is exclusively determined by disorder and the corresponding fixed point is the isotropic version of the so-called infinite randomness fixed point, which is realized in random quantum spin chains. From this mapping we conjecture the values of the critical exponents as beta=2- d(f), beta(s) =1/2, and nu=1.

arXiv:cond-mat/0312532•Physical Review E•May 24, 2004•25 citations

Phase transition properties of three-dimensional systems described by diluted potts model

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

Monte Carlo simulations are performed to analyze phase transitions in three-dimensional systems described by the 3-state Potts model with nonmagnetic impurities. Numerical results are presented for systems with spin concentrations p = 1.00, 0.95, 0.90, 0.80, 0.70, and 0.65 on lattices of size L varying between 20 and 44. Binder’s cumulant analysis shows that the introduction of quenched disorder in the form of non-magnetic impurities induces a crossover from first-order to second-order phase transition. The finite-size scaling method is used to calculate the static critical exponents α, γ, β, and ν for specific heat, susceptibility, magnetization, and correlation length, respectively.

Journal of Experimental and Theoretical Physics•Sep 1, 2009•14 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

Cluster Percolation and First Order Phase Transitions in the Potts Model

Santo Fortunato, Helmut Satz

The q-state Potts model can be formulated in geometric terms, with Fortuin-Kasteleyn (FK) clusters as fundamental objects. For vanishing external field, the phase transition of the model can be equivalently described as a percolation transition of FK clusters. In this work, we investigate numerically the percolation behaviour along the line of first-order phase transitions of the 3d 3-state Potts model in a non-vanishing external field and find that the percolation strength exhibits a discontinuity along the entire line. The endpoint is also a percolation point for the FK clusters, but the corresponding critical exponents are neither in the Ising nor in the random percolation universality class. (C) 2002 Published by Elsevier Science B.V.

•Aug 6, 2001•4 citations

Surface critical exponents at a discontinuous bulk transition

Linjun Li, Michel Pleimling

Systems with a bulk first-order transition can display diverging correlation lengths close to a surface. This surface induced disordering yields a special type of surface criticality. Using extensive numerical simulations we study surface quantities in the two-dimensional Potts model with a large number of states $q$ which undergoes a discontinuous bulk transition. The surface critical exponents are thereby found to depend on the value of $q$, which is in contrast to prior claims that these exponents should be universal and independent of $q$. It follows that surface-induced disordering at first-order transitions is characterized by exponents that depend on the details of the model.

arXiv:1311.3197•Physical Review B•Dec 26, 2013•3 citations
Phase transitions induced by varying the strength of disorder in the large- q state Potts model in 3d are studied by analytical and numerical methods. By switching on the disorder, the transition stays of first order, but different thermodynamical quantities display essential singularities. Only for strong enough disorder will the transition be soften into a second-order one, in which case the ordered phase becomes non-homogeneous at large scales, while the non-correlated sites percolate the sample. In the critical regime the critical exponents are found universal: β/ν = 0.60(2) and ν = 0.73(1).
We study the effect of varying strength $\ensuremath{\delta}$ of bond randomness on the phase transition of the three-dimensional Potts model for large qqq. The cooperative behavior of the system is determined by large correlated domains in which the spins point in the same direction. These domains have a finite extent in the disordered phase. In the ordered phase there is a percolating cluster of correlated spins. For a sufficiently large disorder $\ensuremath{\delta}>{\ensuremath{\delta}}_{t}$ this percolating cluster coexists with a percolating cluster of noncorrelated spins. Such a coexistence is only possible in more than two dimensions. We argue and check numerically that ${\ensuremath{\delta}}_{t}$ is the tricritical disorder, which separates the first- and second-order transition regimes. The tricritical exponents are estimated as ${\ensuremath{\beta}}_{t}∕{\ensuremath{\nu}}_{t}=0.10(2)$ and ${\ensuremath{\nu}}_{t}=0.67(4)$. We claim these exponents are qqq independent for sufficiently large qqq. In the second-order transition regime the critical exponents ${\ensuremath{\beta}}_{t}∕{\ensuremath{\nu}}_{t}=0.60(2)$ and ${\ensuremath{\nu}}_{t}=0.73(1)$ are independent of the strength of disorder.
The phase transition in the q -state Potts model with homogeneous ferromagnetic couplings is strongly first order for large q, while it is rounded in the presence of quenched disorder. Here we study this phenomenon on different two-dimensional lattices by using the fact that the partition function of the model is dominated by a single diagram of the high-temperature expansion, which is calculated by an efficient combinatorial optimization algorithm. For a given finite sample with discrete randomness the free energy is a piecewise linear function of the temperature, which is rounded after averaging, however, the discontinuity of the internal energy at the transition point (i.e., the latent heat) stays finite even in the thermodynamic limit. For a continuous disorder, instead, the latent heat vanishes. At the phase transition point the dominant diagram percolates and the total magnetic moment is related to the size of the percolating cluster. Its fractal dimension is found d(f) = ( 5 + square root of 5)/4 and it is independent of the type of the lattice and the form of disorder. We argue that the critical behavior is exclusively determined by disorder and the corresponding fixed point is the isotropic version of the so-called infinite randomness fixed point, which is realized in random quantum spin chains. From this mapping we conjecture the values of the critical exponents as beta=2- d(f), beta(s) =1/2, and nu=1.
Monte Carlo simulations are performed to analyze phase transitions in three-dimensional systems described by the 3-state Potts model with nonmagnetic impurities. Numerical results are presented for systems with spin concentrations p = 1.00, 0.95, 0.90, 0.80, 0.70, and 0.65 on lattices of size L varying between 20 and 44. Binder’s cumulant analysis shows that the introduction of quenched disorder in the form of non-magnetic impurities induces a crossover from first-order to second-order phase transition. The finite-size scaling method is used to calculate the static critical exponents α, γ, β, and ν for specific heat, susceptibility, magnetization, and correlation length, respectively.
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.
The q-state Potts model can be formulated in geometric terms, with Fortuin-Kasteleyn (FK) clusters as fundamental objects. For vanishing external field, the phase transition of the model can be equivalently described as a percolation transition of FK clusters. In this work, we investigate numerically the percolation behaviour along the line of first-order phase transitions of the 3d 3-state Potts model in a non-vanishing external field and find that the percolation strength exhibits a discontinuity along the entire line. The endpoint is also a percolation point for the FK clusters, but the corresponding critical exponents are neither in the Ising nor in the random percolation universality class. (C) 2002 Published by Elsevier Science B.V.
Systems with a bulk first-order transition can display diverging correlation lengths close to a surface. This surface induced disordering yields a special type of surface criticality. Using extensive numerical simulations we study surface quantities in the two-dimensional Potts model with a large number of states qqq which undergoes a discontinuous bulk transition. The surface critical exponents are thereby found to depend on the value of qqq, which is in contrast to prior claims that these exponents should be universal and independent of qqq. It follows that surface-induced disordering at first-order transitions is characterized by exponents that depend on the details of the model.