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The surface and bulk properties of the two-dimensional Q > 4 state Potts model in the vicinity of the first order bulk transition point have been studied by exact calculations and by density matrix renormalization group techniques. For the surface transition the complete analytical solution of the problem is presented in the $Q to infty$ limit, including the critical and tricritical exponents, magnetization profiles and scaling functions. According to the accurate numerical results the universality class of the surface transition is independent of the value of Q > 4. For the bulk transition we have numerically calculated the latent heat and the magnetization discontinuity and we have shown that the correlation lengths in the ordered and in the disordered phases are identical at the transition point.
We studied the non-equilibrium dynamics of the q-state Potts model in the square lattice, after a quench to sub-critical temperatures. By means of a continuous time Monte Carlo algorithm (non-conserved order parameter dynamics) we analyzed the long t
We demonstrate that the occurrence of symmetry breaking phase transitions together with the emergence of a local order parameter in classical statistical physics is a consequence of the geometrical structure of probability space. To this end we inves
The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described by the top
Monte Carlo simulations are performed to study the two-dimensional Potts models with q=3 and 4 states on directed Small-World network. The disordered system is simulated applying the Heat bath Monte Carlo update algorithm. A first-order and second-or
The continuous ferromagnetic-paramagnetic phase transition in the two-dimensional Ising model has already been excessively studied by conventional canonical statistical analysis in the past. We use the recently developed generalized microcanonical in