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Critical properties of the three-state Potts model on two-dimensional lattices: A finite-size scaling study

Muhammet Arucu

Physica A Statistical Mechanics and its ApplicationsOct 1, 20260 citations

Finite-size-scaling study of the simple cubic three-state Potts glass: Possible lower critical dimensiond=3

M. Scheucher, Joseph D. Reger, Kurt Binder +1 more

For small lattices with linear dimension L ranging from L=3 to L=8 we obtain the distribution function P(q) of the overlap q between two real replicas of the three-state Potts-glass model with symmetric nearest-neighbor interaction with a Gaussian distribution. A finite-size-scaling analysis suggests a zero-temperature transition to occur with an exponentially diverging correlation length ${\ensuremath{\xi}}_{\mathrm{SG}}$\ensuremath{\sim}exp(C/${\mathit{T}}^{\mathrm{\ensuremath{\sigma}}}$). This implies that d=3 is the lower critical dimension.For small lattices with linear dimension L ranging from L=3 to L=8 we obtain the distribution function P(q) of the overlap q between two real replicas of the three-state Potts-glass model with symmetric nearest-neighbor interaction with a Gaussian distribution. A finite-size-scaling analysis suggests a zero-temperature transition to occur with an exponentially diverging correlation length ${\ensuremath{\xi}}_{\mathrm{SG}}$\ensuremath{\sim}exp(C/${\mathit{T}}^{\mathrm{\ensuremath{\sigma}}}$). This implies that d=3 is the lower critical dimension.

Physical review. B, Condensed matterOct 1, 199046 citations

Finite-Size Scaling Study of the Three-State Potts Model in Random Fields: Evidence for a Second-Order Transition

K Eichhorn, Kurt Binder

Three-state Potts ferromagnets on the simple cubic lattice in random fields are studied by extensive Monte Carlo simulation. The implications of the possible hyperscaling violation to finite-size scaling are discussed. Evidence for a second-order transition is obtained, as well as rough estimates for critical exponents. A qualitative phase diagram is proposed compatible with the predictions of Blankschtein et al. on the random field-induced shift of the tricritical curve q = q c ( d ) in the plane of variables dimensionality d and number of states q .Three-state Potts ferromagnets on the simple cubic lattice in random fields are studied by extensive Monte Carlo simulation. The implications of the possible hyperscaling violation to finite-size scaling are discussed. Evidence for a second-order transition is obtained, as well as rough estimates for critical exponents. A qualitative phase diagram is proposed compatible with the predictions of Blankschtein et al. on the random field-induced shift of the tricritical curve q = q c ( d ) in the plane of variables dimensionality d and number of states q .

Europhysics Letters (EPL)May 20, 199522 citations

Finite-size effects and phase transition in the three-dimensional three-state Potts model

O. F. de Alcantara Bonfim

Journal of Statistical PhysicsJan 1, 199113 citations

Logarithmic corrections to finite-size scaling in the four-state Potts model

Chris J. Hamer, Murray T. Batchelor, Michael N. Barber

Journal of Statistical PhysicsAug 1, 198841 citations

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 .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 PhysicsMay 1, 20071 citation

Finite-size scaling of the three-state Potts model on a simple cubic lattice

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