We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class.
We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class.
We apply simulated tempering and magnetizing (STM) Monte Carlo simulations to the two-dimensional threestate Potts model in an external magnetic field in order to investigate the crossover scaling behaviour in the temperature-field plane at the Potts critical point and towards the Ising universality class for negative magnetic fields.Our data set has been generated by STM simulations of several square lattices with sizes up to 160×160 spins, supplemented by conventional canonical simulations of larger lattices at selected simulation points.We present careful scaling and finite-size scaling analyses of the crossover behaviour with respect to temperature, magnetic field and lattice size.
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.
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.
The q-state Potts model on a square lattice and in the presence of an external magnetic field that couples to only one state is studied by using extensive Monte Carlo simulations. A hybrid algorithm that combines the single spin-flip Metropolis method with Wolff cluster updates is employed. Single-histogram reweighting techniques and the field-mixing approach are also used to obtain the corresponding universal probability distributions. By analyzing the finite-size scaling behavior of the order parameters and universal probability distributions, the phase diagram in the temperature-versus-external field plane is obtained in the thermodynamic limit for some values of state q≥5. For positive fields and higher values of q, there is a clear first-order transition line that starts at the zero-field transition point and ends at an isolated critical point, which is in the two-dimensional Ising universality class. As the value of state q decreases, the corresponding critical field also decreases. The present results strongly suggest that the critical field vanishes when q→5^{+}. However, for negative fields, another first-order transition line occurs without any critical or multicritical behavior for q≥6. The special case with q=5 undergoes a weak first-order transition at zero field and a line of second-order transitions for negative fields. This second-order transition line is in the same universality class as the q=4 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.
Spin systems exposed to the influence of random magnetic fields are paradigmatic examples for studying the effect of quenched disorder on condensed-matter systems. In this context, previous studies have almost exclusively focused on systems with Ising or continuous symmetries, while the Potts symmetry, albeit being of fundamental importance also for the description of realistic physical systems, has received very little attention. In the present study, we use a recently developed quasiexact method for determining ground states in the random-field Potts model to study the problem with four states. Extending the protocol applied for the three-state model, we use extensive finite-size scaling analyses of the magnetization, Binder parameter, energy cumulant, specific heat, and the connected as well as disconnected susceptibilities to study the magnetic ordering transition of the model. In contrast to the system in the absence of disorder, we find compelling evidence for a continuous transition, and we precisely determine the critical point as well as the critical exponents, which are found to differ from the exponents of the three-state system as well as from those of the random-field Ising model.