Configurations and observables in an Ising model with heat flow

Abstract

We study a two dimensional Ising model between thermostats at different temperatures. By applying the recently introduced KQ dynamics, we show that the system reaches a steady state with coexisting phases transversal to the heat flow. The relevance of such complex states on thermodynamic or geometrical observables is investigated. In particular, we study energy, magnetization and metric properties of interfaces and clusters which, in principle, are sensitive to local features of configurations. With respect to equilibrium states, the presence of the heat flow amplifies the fluctuations of both thermodynamic and geometrical observables in a domain around the critical energy. The dependence of this phenomenon on various parameters (size, thermal gradient, interaction) is discussed also with reference to other possible diffusive models.

Surface Criticality at a Dynamic Phase Transition

“…Whereas in some instances, as for example paradigmatic transport models [1] or driven diffusive systems [2], notable progress has been achieved in understanding nonequilibrium steady states, a common theoretical framework remains elusive. This is especially true in cases where steady states are influenced by the presence of surfaces or interfaces, which can change properties even deep inside the bulk [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].Nonequilibrium phase transitions form an interesting class of phenomena that share many commonalities with their equilibrium counterparts. For example, for continuous transitions different universality classes, characterized by different sets of critical exponents, have been identified.…”

Microscopic energy flows in disordered Ising spin systems

“…), where the previous, theoretical approaches get an applicative relevance [1,2,3,4]. Discrete models, from simple or interactive random walks to classical spin models, play an important role for all such questions [5,6,7,8,9,10,11,12]. In particular, here we deal with an Ising system coupled with thermostats imposing an energy flow, and we study its behavior at microscopic scales.…”

Interacting random walkers and non-equilibrium fluctuations

“…This constitutes an interesting result, especially in comparison with the spin system mentioned above [10,11]. There are relevant analogies: the spin flip in Ising and the jump probability in RW both depend on " link properties " (energy and link populations, respectively); both systems display a pseudo-critical parameter (the critical temperature or energy, say E c , and the population N c , respectively).…”

“…Actually, this kind of behaviour was revealed in different fields -magnetic systems, biology, reactiondiffusion processes (see for example [4,5,6,7]). On a more modellistic ground, we may quote a recently studied 2-dimensional Ising system between two thermostats, where heat transport exhibits indeed an energy dependent diffusivity [8,9,10,11].…”