Depinning of a domain wall in the 2d random-field Ising model

Abstract

We report studies of the behaviour of a single driven domain wall in the 2-dimensional non-equilibrium zero temperature random-field Ising model, closely above the depinning threshold. It is found that even for very weak disorder, the domain wall moves through the system in percolative fashion. At depinning, the fraction of spins that are flipped by the proceeding avalanche vanishes with the same exponent beta=5/36 as the infinite percolation cluster in percolation theory. With decreasing disorder strength, however, the size of the critical region decreases. Our numerical simulation data appear to reflect a crossover behaviour to an exponent beta'=0 at zero disorder strength. The conclusions of this paper strongly rely on analytical arguments. A scaling theory in terms of the disorder strength and the magnetic field is presented that gives the values of all critical exponent except for one, the value of which is estimated from scaling arguments.Comment: 13 pages Revtex, 13 eps figure

Percolation transitions in the survival of interdependent agents on multiplex networks, catastrophic cascades, and solid-on-solid surface growth

“…This is e.g. what is found in the T = 0 random field Ising model [58,59], and such interfaces seem always to be in the OP universality class, even if they look very smooth on small scales [61].…”

“…In d ≥ 3 there exist indeed tricritical points in generalized percolation models where the phase transition changes from second to first order [9,10]. There is however strong evidence [10,58,59] that such tricritical points are absent in d = 2. This seems related to the Aizenman-Wehr theorem [60] on absence of first order phase transitions in random 2-d systems, although details are far from clear.…”

Attacks and infections in percolation processes

“…Several years ago, we generalized the GEP to the EGEP to allow, besides critical percolation, for tricritical and firstorder percolation transitions, which had been predicted earlier from simulations in the context of depinning transitions of driven surfaces in random media at zero temperature [10]. Simulations also showed that tricritical and first-order percolation disappear below three spatial dimensions in random media depinning [11] as well as in direct simulations of the EGEP [12].…”

Influence of the aspect ratio and boundary conditions on universal finite-size scaling functions in the athermal metastable two-dimensional random field Ising model

“…Seppälä et al [21] found evidence of front roughening effects in the equilibrium RFIM at T = 0 with FBC without external field. The model with metastable dynamics but restricted to nucleation close to the interface, was studied in the context of depinning transition [22], and for the study of morphological changes in the invading front [23]. The ground state of the equilibrium 3d-RFIM was studied by Middelton and Fisher using a variety of fixed boundary conditions and comparing with periodic boundaries [24] In this work, we present a numerical study of the number of 1d-spanning avalanches N 1 in the metastable twodimensional RFIM using the two strategies described above.…”