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We study the stochastic dynamics of infinitely many globally interacting $q$-state units on a ring that is externally driven. While repulsive interactions always lead to uniform occupations, attractive interactions give rise to much richer phenomena: We analytically characterize a Hopf bifurcation which separates a high-temperature regime of uniform occupations from a low-temperature one where all units coalesce into a single state. For odd $q$ below the critical temperature starts a synchronization regime which ends via a second phase transition at lower temperatures, while for even $q$ this intermediate phase disappears. We find that interactions have no effects except below critical temperature for attractive interactions. A thermodynamic analysis reveals that the dissipated work is reduced in this regime, whose temperature range is shown to decrease as $q$ increases. The $q$-dependence of the power-efficiency trade-off is also analyzed.
A new classification of sandpile models into universality classes is presented. On the basis of extensive numerical simulations, in which we measure an extended set of exponents, the Manna two state model [S. S. Manna, J. Phys. A 24, L363 (1991)] is
We investigate the two-dimensional $q=3$ and 4 Potts models with a variable interaction range by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges as expressed by the number $z$ of equivalent neighbors.
We consider the problem of inferring a graphical Potts model on a population of variables, with a non-uniform number of Potts colors (symbols) across variables. This inverse Potts problem generally involves the inference of a large number of paramete
We study the effect of interfacial phenomena in two-dimensional perfect and random (or disordered) $q$-state Potts models with continuous phase transitions, using, mainly, Monte Carlo techniques. In particular, for the total interfacial adsorption, t
Phase transition of the two- and three-state quantum Potts models on the Sierpinski pyramid are studied by means of a tensor network framework, the higher-order tensor renormalization group method. Critical values of the transverse magnetic field and