Depinning transition of a driven interface in the random-field Ising model around the upper critical dimension

Abstract

We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal fluctuations. Although thermal fluctuations drive the system away from criticality the order parameter obeys a certain scaling law for sufficiently low temperatures and the corresponding exponents are determined. Our results suggest that the so-called upper critical dimension of the depinning transition is five and that the systems belongs to the universality class of the quenched Edward-Wilkinson equation.

Universal Scaling Behavior of Directed Percolation Around the Upper Critical Dimension

“…The logarithmic correction exponents B and Σ are characteristic features of the whole universality class similar to the usual critical exponents. Numerous theoretical, numerical, as well as experimental investigations of critical systems at D c have been performed (see for instance [46,47,48,49,50,26,27,28,23,32,33]).…”

Random-Field Ising Models of Hysteresis

“…Katzgraber et al show that this memory effect emerges in the nonequilibrium Edwards Anderson spin glass (EASG) when the magnetic field is first decreased from its saturation value and then increased again from some reversal field H R . The authors find that EASG exhibits a singularity at the negative of the reversal field, 17 The complementary point memory relates the magnetic domains at one point on the major hysteresis loop to the domains at the complementary point on the major loop during the same and during subsequent cycles.…”

“…On the other hand, the absence of exact (microscopic) return point memory has also been observed (61; 62; 63), and there are various interesting experiments testing for the reproducibility of magnetic avalanches (64; 65; 66) and for microscopic return point memory and complementary point memory in magnets at various disorders (67). 17 In (67) the authors experimentally study the influence of disorder on major loop return point memory and complementary return point memory in Co/Pt samples with varying interfacial roughness and find with increasing disorder the onset and saturation of both return point memory and complementary point memory.…”

Morphological transitions in supercritical generalized percolation and moving interfaces in media with frozen randomness

“…For small roughnesses, i.e., far above the percolation threshold, we could simulate systems with base surfaces up to L × L = 8192 × 8192 and followed them typically for 2 × 10 5 time steps (for smaller base surfaces, up to L = 2048, we went up to 10 6 to 10 7 time steps). This is to be compared to the largest previous simulation of interfaces with overhangs (in the RFIM), where t ≈ L 250 [34].…”

“…far above the percolation threshold, we could simulate systems with base surfaces up to L × L = 8192 × 8192 (although we shall present here results only for L ≤ 4096), and followed them typically for 10 6 to t0 7 time steps. This is to be compared to the largest previous simulation of interfaces with overhangs (in the RFIM) , where t ≈ L ≤ 250 [25].…”