Monte Carlo study of a kinetic lattice model with random diffusion of disorder

Nonequilibrium phase transitions and tricriticality in a three-dimensional lattice system with random-field competing kinetics

“…where stands for MC or time average [21]. As discussed in [20], the susceptibility peaks positions grow with the system size as…”

“…Concerning spin glasses, for example, quenched models like the Edwards-Anderson (EA) [24] neglect the diffusion of magnetically active ions. Diffusion constantly modifies the distance between each specific pair of spin ions in certain substances like dilute metallic alloys (CuMn, for example) and, consequently, one should probably allow for variations both in space and time of the exchange interactions in a model [21]. In the same way, we can imagine other disordered systems in which the random variables change in space and time, like random-field models.…”

“…While annealed and quenched versions of the RFIM predict continuous phase transitions between the ordered and disordered phases [13,14,26] 2 , measurements on diluted antiferromagnets like Fe x Mg 1−x Cl 2 , which are prototypes of experimental realizations of systems under random fields [2], showed that these materials exhibit first-order phase transitions at low temperatures [27]. [1] The nonequilibrium Ising spin glass was studied via MC simulations in [21]. [2] There are some controversies about the order of the low-temperature phase transition in the RFIM, but recent simulations suggest the occurrence of continuous transitions [13,14].…”

Ferromagnetic and spin-glass-like transition in the majority vote model on complete and random graphs

“…In the case of models which possess Hamiltonian, as in equation 1, but are out of equilibrium due to contact with several thermal baths with different temperatures the above-mentioned equivalence can be revealed by finding effective temperature T ef f = 1/β ef f , and the respective Gibbs distribution is that with T ef f and energy given by the Hamiltonian of the model [28,29]. Most analytic and numerical results concerning such equivalence were obtained for spin models on regular d-dimensional lattices with competing spin flip mechanisms [28][29][30][31][32][33][34][35][36][37], but they can be easily extended to similar models on RRGs since in both cases the degrees of nodes obey a one-point distribution P (k) = δ k,K . For example, let us consider a model with the spin flip rate (2) being a combination of two Glauber rates with temperatures T 1 , T 2 .…”

“…Thus, the following investigation of the SG-like transition in the MV model is based mainly on MC simulations. In contrast, FM and possibly AFM transitions in nonequilibrium models with competing spin flip mechanisms and different kinds of disorder have been broadly studied in spin models, mainly on regular lattices [28][29][30][31][32][33][34][35][36][37], analytically using the concept of the effective Hamiltonian [28][29][30]32], a sort of pair approximation (PA) [31] and numerically via MC simulations [33][34][35][36][37]; the latter studies comprised also models with MV kind of dynamics [34,35]. It should be, however, mentioned that the concept of the effective Hamiltonian in certain special cases can be also useful in the analytic study of other nonequilibrium systems, e.g., neural networks with fast time variation of synapses in which both the FM and SG phases can occur [38].…”