Sheared Ising models in three dimensions

Abstract

The nonequilibrium phase transition in sheared three-dimensional Ising models is investigated using Monte Carlo simulations in two different geometries corresponding to different shear normals. We demonstrate that in the high shear limit both systems undergo a strongly anisotropic phase transition at exactly known critical temperatures Tc which depend on the direction of the shear normal. Using dimensional analysis, we determine the anisotropy exponent θ = 2 as well as the correlation length exponents ν = 1 and ν ⊥ = 1/2. These results are verified by simulations, though considerable corrections to scaling are found. The correlation functions perpendicular to the shear direction can be calculated exactly and show Ornstein-Zernike behavior.

Model of magnetic friction obeying the Dieterich-Ruina law in the steady state

“…(1) are constants for usual solids, whereas B depends on the system size by L ′ x in Eq. (14). However, we cannot identify what causes this difference by this study alone.…”

“…Previous studies have already proposed models in which two lattices interact with each other [11][12][13][14][15]. However, in our model the shift of the upper lattice δx changes according to Eq.…”

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.…”

Surface critical exponents at a discontinuous bulk transition

“…Related surface (or, more appropriately, interface) phenomena are also encountered in non-equilibrium situations where magnetic systems are sheared or magnetic blocks are moved passed each other, thereby giving rise to magnetic friction [20][21][22][23][24][25]. When the involved bulk systems have an equilibrium first-order transition, as it is the case for two-dimensional and three-dimensional Potts system with a large number of states, non-equilibrium surface transitions of different types (continuous, discontinuous, tricritical) emerge [22,25].…”