Nonequilibrium phase transition in a driven Potts model with friction

Abstract

We consider magnetic friction between two systems of q-state Potts spins which are moving along their boundaries with a relative constant velocity ν. Due to the interaction between the surface spins there is a permanent energy flow and the system is in a steady state, which is far from equilibrium. The problem is treated analytically in the limit ν=∞ (in one dimension, as well as in two dimensions for large-q values) and for v and q finite by Monte Carlo simulations in two dimensions. Exotic nonequilibrium phase transitions take place, the properties of which depend on the type of phase transition in equilibrium. When this latter transition is of first order, a sequence of second- and first-order nonequilibrium transitions can be observed when the interaction is varied.

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.…”

Spin waves cause non-linear friction

“…Two classes of models have been considered, which show different phenomena. The first one is Ising-like spin systems with two equivalent half spaces moving relative to each other [4][5][6][7][8]. In this case, friction is induced by thermal fluctuations, and hence is not present at zero temperature.…”

Effects of boundary conditions on magnetic friction

“…Several experimental facts suggest that physical degrees of freedom, such as phonon [14][15][16][17][18][19][20], orbital motion of electrons [20][21][22][23] and magnetic moment of spins [24,25], play roles of dissipation channels. Especially for the magnetic moment, Monte Carlo simulations of classical spin systems by the use of the Monte Carlo simulations and the analysis based on the Landau-Lifshitz-Gilbert equation [26][27][28][29][30][31][32][33][34][35][36][37] have revealed several facts regarding the friction due to magnetism from the viewpoints of statistical mechanics.…”

“…Many facts with the magnetic friction have been revealed, but almost all of them are related to the model of infinite size ( Fig. 1(a)) [28,30,31,33,35,37], where almost exclusively nonequilibrium phase transitions are discussed. In order to understand the non-equilibrium nature of classical spin systems, however, finite-size extension is one of the most important directions.…”