The standard Potts model is investigated in the framework of nonextensive statistical mechanics. We performed Monte Carlo simulations on two-dimensional lattices with linear sizes ranging from 16 to 64 using the Metropolis algorithm, where the classical Boltzmann-Gibbs transition probabilities were modified for the nonextensive case. We found that the Potts model undergoes a phase transition in the nonextensive scenario. We established the order of the phase transition and we computed the critical temperature for different values of the Tsallis entropic index.
The fluctuations of thermodynamic systems in the presence of the fields are considered. The approach is of phenomenological nature and developed in a Gaussian approximation. The cases of a magnetizable continuum in a magnetoquasistatic field, as well as the so called discrete systems are used to exemplify the study. In the latter case one finds that the fluctuation estimators depend both on the intrinsic properties of the system and on the characteristics of the environment. Following earlier ideas of one of the authors we present a class of thermodynamic inequalities for the systems investigated in this paper. In the case of two variables these inequalities are nonquantum analogs of the well known quantum Heisenberg "uncertainty" relations. In this context, the fluctuation estimators support the idea that Boltzmann's constant k has the signification of a generic indicator of stochasticity for thermodynamic systems.
The higher-order moments of the fluctuations for thermodynamic systems in the presence of fields are investigated in the framework of a theoretical method. The method uses a generalized statistical ensemble consistent with an adequate expression for the internal energy. The applications refer to the case of a system in a magnetoquasistatic field. In the case of linear magnetic media, one finds that, for the description of the magnetic induction fluctuations, the Gaussian approximation is satisfactory. For nonlinear media, the corresponding fluctuations are non-Gaussian, having a non-null asymmetry. Furthermore, the respective fluctuations have characteristics of leptokurtic, mesokurtic and platykurtic type, depending on the value of the magnetic field strength as compared with a scaling factor of the magnetization curve.
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