Phase transitions and critical phenomena in a three-dimensional site-diluted Potts model

The phase transitions and critical phenomena in the three-dimensional (3D) site-diluted q-state Potts models on a simple cubic lattice are explored. We systematically study the phase transitions of the models for q=3 and q=4 on the basis of Wolff high-effective algorithm by the Monte–Carlo (MC) method. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p=1.00–0.65. It is shown that introducing of weak disorder (p∼0.95) into the system is sufficient to change the first order phase transition into a second order one for the 3D 3-state Potts model, while for the 3D 4-state Potts model, such a phase transformation occurs when introducing strong disorder (p∼0.65). Results for 3D pure 3-state and 4-state Potts models (p=1.00) agree with conclusions of mean field theory. The static critical exponents of the specific heat α, susceptibility γ, magnetization β, and the exponent of the correlation radius ν are calculated for the samples on the basis of finite-size scaling theory.     

Features of the phase transitions in the three-dimensional diluted potts model with number of spin states <Emphasis Type="Italic">q</Emphasis> = 3

The effect of frozen disorder, implemented in the form of nonmagnetic impurities, on phase transitions in the three-dimensional Potts model with number of states q = 3 has was investigated by the Monte Carlo method, using the Wolf single-cluster algorithm. Systems with linear sizes L = 20–44 were considered at spin concentrations p = 1.00–0.65. The method of fourth-order Binder cumulants was used to demonstrate that a first-order phase transition is observed for the pure model (p = 1.00) and a second-order phase transition occurs at concentrations p = 0.90, 0.80, 0.70, and 0.65.     

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

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.     

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

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.     

Investigation of the influence of quenched nonmagnetic impurities on phase transitions in the three-dimensional Potts model

The influence of quenched nonmagnetic impurities on phase transitions in the three-dimensional Potts model with the number of spin states q = 3 is investigated using the Wolff single-cluster algorithm of the Monte Carlo method. The systems with linear sizes L = 20–44 at the spin concentrations p = 1.0, 0.9, 0.8, and 0.7 are analyzed. It is demonstrated with the use of the method of fourth-order Binder cumulants that the second-order phase transition occurs in the model under consideration at the spin concentrations p = 0.9, 0.8, and 0.7 and that the first-order phase transition is observed in the pure model (p = 1.0). The static critical exponents α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length) are calculated in the framework of the finite-size scaling theory. The problem regarding the universality classes of the critical behavior of weakly diluted systems is discussed.     

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

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.     

Investigation of the critical properties of the three-dimensional weakly diluted potts model

The problem of the type of the phase transition in the three-dimensional weakly diluted Potts model with the number of spin states q= 3 has been investigated by the Monte Carlo method. The temperature dependences of the Binder cumulants, energy, magnetization, specific heat, and susceptibility have been calculated. It is found that the second-order phase transition occurs in a system at the spin concentration p = 0.9. The critical exponents of the magnetization (β), specific heat (α), and susceptibility (γ) and the critical correlation-length exponent v were calculated on the basis of the finite-size scaling theory at p = 0.9.     

Three-dimensional 3-state Potts model revisited with new techniques

We report a fairly detailed finite-size scaling analysis of the first-order phase transition in the three-dimensional 3-state Potts model on cubic lattices with emphasis on recently introduced quantities whose infinite-volume extrapolations are governed only by exponentially small terms. In these quantities no asymptotic power series in the inverse volume are involved which complicate the finite-size scaling behaviour of standard observables related to the specific-heat maxima or Binder-parameter minima. Introduced initially for strong first-order phase transitions in q-state Potts models with “large enough” q, the new techniques prove to be surprisingly accurate for a q value as small as 3. On the basis of the high-precision Monte Carlo data of Alves et al. [Phys. Rev. B 43 (1991) 5846], this leads to a refined estimate of β_t = 0.550 565(10) for the infinite-volume transition point.     

Influence of quenched nonmagnetic impurities on phase transitions in a three-dimensional diluted Potts model with spin state number q = 4

The influence of quenched nonmagnetic impurities on phase transitions and critical phenomena in the 3D Potts model with the spin state number q = 4 is studied using the Monte Carlo method. Systems with the linear size L = 20–32 and spin concentrations p = 1.00, 0.90, 0.65 are considered. The fourth order Binder cumulant method is used to demonstrate that in the strongly diluted regime, a phase transition of the second kind is observed in this model for the spin concentration p = 0.65, and a phase transition of the first kind is observed for the pure (p = 1.00) and weakly diluted (p = 0.90) models. The theory of finite-dimensional scaling is used to calculate the static critical parameters of heat capacity α, susceptibility γ, magnetization β, and correlation radius ν.     

Tricritical point of the three-dimensional Potts model (q = 4) with quenched nonmagnetic disorder

The effect of quenched nonmagnetic impurities on the phase transitions in the three-dimensional Potts model with the number of spin states q = 4 for the case of the simple cubic lattice is studied using the Monte Carlo method. The phase transitions in this model are studied for spin density p ranging from 1.0 to 0.70. The position of the tricritical point at the phase diagram is determined.     

First-order phase transitions and integrable field theory. The dilute q-state Potts model

We consider the two-dimensional dilute q-state Potts model on its first-order phase transition surface for 0 < q ⩽ 4. After determining the exact scattering theory which describes the scaling limit, we compute the two-kink form factors of the dilution, thermal and spin operators. They provide an approximation for the correlation functions whose accuracy is illustrated by evaluating the central charge and the scaling dimensions along the tricritical line.     

Monte Carlo study of the phase transitions in 2D ferro- and antiferromagnetic Potts models on a triangular lattice

The phase transitions in 2D ferro- and antiferromagnetic Potts models with number of spin states q = 3 on a triangular lattice are investigated by the cluster and classical Monte Carlo methods. Systems with linear sizes L = 20–120 are considered. Fourth-order Binder cumulants and histogram data analysis are used to show that second- and first-order phase transitions are observed in the ferromagnetic and antiferromagnetic Potts models, respectively. The static critical indices are calculated for specific heat α, susceptibility γ, magnetization β, and correlation length ν on the basis of finite-size scaling theory for a ferromagnetic Potts model.     

The Kadanoff lowerbound renormalization transformation for the q-state Potts model

The Kadanoff lowerbound renormalization transformation when applied to the 2-dimensional q-state Potts model, is found to show a bifurcation phenomenon at q = 4, that might be considered as signalling the onset to the first-order transition. At the value of the free parameter where the bifurcation is found, the specific heat exponent takes almost the value predicted by weak universality $\text{α(4) =}\text{2}\text{3}$, while the cross-over exponent in the Potts-lattice gas direction becomes marginal. The cross-over exponent in the cubic direction is found already to be irrelevant for q > 3.3. Further a duality relation for a class of models obtained by a partial breaking of the Potts symmetry in the hamiltonian, including the cubic model is derived.     

The potts model on bethe lattices

We analyze the properties of theq-state ferromagnetic Potts model for realq. The nature of the phase transition at the critical point is first-order forq2, and second-order forq=2. The random-bond percolation limitq1, and its second-order-like transition, are not related to the previous behaviour since they arise from non-stable phases of the system. It is suggested that this property characterizes the model on high-dimensional lattices, too.Supported by MPI and CNR     

Phase transitions in three-dimensional three-state Potts model

We have performed a Monte Carlo investigation of the nature of the phase transition in the three-state, three-dimensional Potts model with nearest and next nearest neighbour coupling. We find strong evidence for a first-order phase transition in the case of ferromagnetic coupling. In the case of a first neighbour ferromagnetic coupling and second neighbour antiferromagnetic, there is evidence for a second-order transition. This result supports the idea that a second-order transition can be present in systems which, according to the Landau criterium, should only undergo a first-order transition.     

On Dynamical Systems and Phase Transitions for q + 1-state p-adic Potts Model on the Cayley Tree

In the present paper, we study a new kind of p-adic measures for q?+?1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider two mode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition.     

Determination of the phase structure of the four-dimensional coupled gauge-Higgs Potts model

Using Monte Carlo simulations the phase structure of the four-dimensional N-state gauge Potts model coupled to Higgs fields is determined. A three-phase diagram is established. In the Z(2) case, a first and a second-order transition lines are present. For Z(5) and Z(10) only first-order transition lines appear. The results are consistent with previous mean field predictions.     

Phase structure of QCD at high temperature with massive quarks and finite quark density: A Z(3) paradigm

The confinement/deconfinement phase transition in SU(3) lattice gauge theories at high temperatures is analogous to that of the Z(3) gauge theories. We study various Z(3) gauge-matter theories that result from replacing the gauge group SU(3) with its center Z(3). We include large-mass fermions in the Wilson formulation and allow a chemical potential. We show that in the limit of strong coupling and high temperature the (3 + 1)-dimensional theory becomes a three state, three-dimensional Potts model with uniform external fields of real and imaginary strengths related to the fermion mass and chemical potential. By studying the phase structure of the q = 3, d = 3 Potts model with external fields we argue that the confinement/deconfinement phase transition is first order, but highly sensitive to external fields, and that it does not occur at “strong coupling” in a Z(3) gauge theory if there is a light enough fermion present. We discuss the consequences of this result for QCD.     

First-order phase transition in the graphite compound LiC6

Elastic neutron scattering and scanning calorimetry reveal a weakly first-order “melting” of the Li layers in the graphite intercalation compound LiC₆ at T₀ = 715.4 K, in excellent agreement with recent experiment with recent experiments by Robinson and Salamon. The first-order nature of the transition also agrees with a prediction by Bak and Domany derived from Landau expansions, but the detailed behavior of the fluctuation-induced power-law precursor differs from recent Monte Carlo simulations of the 3D?3q Potts model.     

First-order phase transitions in large entropy lattice models

We show the existence of a first-order phase transition in thev-dimensional Potts model forv≧2, when the number of states of a single spin is big enough. Low-temperature pure phases are proved to survive up to the critical temperature. Also the existence of a first-order transition in thev-dimensional Potts gauge model,v≧3, is obtained if the underlying gauge group is finite but large.