Tricritical behavior of nonequilibrium Ising spins in fluctuating environments

Abstract

We investigate the phase transitions in a coupled system of Ising spins and a fluctuating network. Each spin interacts with q neighbors through links of the rewiring network. The Ising spins and the network are in thermal contact with the heat baths at temperatures T_{S} and T_{L}, respectively, so the whole system is driven out of equilibrium for T_{S}≠T_{L}. The model is a generalization of the q-neighbor Ising model [A. Jędrzejewski et al., Phys. Rev. E 92, 052105 (2015)PLEEE81539-375510.1103/PhysRevE.92.052105], which corresponds to the limiting case of T_{L}=∞. Despite the mean-field nature of the interaction, the q-neighbor Ising model was shown to display a discontinuous phase transition for q≥4. Setting up the rate equations for the magnetization and the energy density, we obtain the phase diagram in the T_{S}-T_{L} parameter space. The phase diagram consists of a ferromagnetic phase and a paramagnetic phase. The two phases are separated by a continuous phase transition belonging to the mean-field universality class or by a discontinuous phase transition with an intervening coexistence phase. The equilibrium system with T_{S}=T_{L} falls into the former case while the q-neighbor Ising model falls into the latter case. At the tricritical point, the system exhibits the mean-field tricritical behavior. Our model demonstrates a possibility that a continuous phase transition turns into a discontinuous transition by a nonequilibrium driving. Heat flow induced by the temperature difference between two heat baths is also studied.

Phase Transitions in the Kinetic Ising Model on the Temporal Directed Random Regular Graph

“…It has been shown that on contrary to the models investigated previously by Lee et al [1], the kinetic model studied in Jȩdrzejewski et al [3] is an non-equilibrium one and corresponds to the infinite temperature T L of links. Furthermore, it has occurred that there is a critical temperature T * L at which switch from discontinuous to continuous phase transition is observed (so called tricritical point) [4]. However, the question arose if such a tricriticality could be exclusively explained on the basis of non-equilibrium driving.…”

“…Therefore results obtained in Jȩdrzejewski et al [3], showing that kinetic Ising model with Metropolis dynamics can also display discontinuous phase transitions, were puzzling and confusing. To solve this puzzle a new generalized model with two heat baths-one for the Ising spins at temperature T s and second for links of the graph at temperature T L , has been recently proposed [4]. It has been shown that on contrary to the models investigated previously by Lee et al [1], the kinetic model studied in Jȩdrzejewski et al [3] is an non-equilibrium one and corresponds to the infinite temperature T L of links.…”

“…It has been shown that on the annealed non-equilibrium network, which within the generalized model by Park and Noh [4] corresponds to the infinite temperature of links (T L = ∞), different dynamics leads to completely different results. For example, the model with heat-bath algorithm at T L = ∞ displays a continuous phase transition, and the critical temperature only slightly deviates from the equilibrium one.…”

“…In Park and Noh [4] it has been introduced by the additional heat-bath for links, whereas in Jȩdrzejewski et al [5] it has been introduced by the probability of flip in the absence of the energy changes W 0 : in the original Metropolis algorithm W 0 = 1, whereas for the heat-bath dynamics W 0 = 1/2. Within the generalized zero-temperature Glauber dynamics, W 0 can change continuously [6], which leads to very interesting results [7][8][9].…”

“…It has been also observed that generally higher flipping probabilities lead to discontinuous phase transitions. Furthermore, based on results obtained within generalized model with two heat-baths [4] and modified Metropolis algorithm studied in Jȩdrzejewski et al [5], it has been suggested that tricriticality, i.e., switch from continuous to discontinuous phase transitions is driven by noise.…”