TheT= 0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states

Abstract

Abstract.In order to elucidate the relationship between rate-independent hysteresis and metastability in disordered systems driven by an external field, we study the Gaussian RFIM at T = 0 on regular random graphs (Bethe lattice) of finite connectivity z and compute to O(1/z) (i.e. beyond mean-field) the quenched complexity associated with the one-spin-flip stable states with magnetization m as a function of the magnetic field H. When the saturation hysteresis loop is smooth in the thermodynamic limit, we find that it coincides with the envelope of the typical metastable states (the quenched complexity vanishes exactly along the loop and is positive everywhere inside). On the other hand, the occurence of a jump discontinuity in the loop (associated with an infinite avalanche) can be traced back to the existence of a gap in the magnetization of the metastable states for a range of applied field, and the envelope of the typical metastable states is then reentrant. These findings confirm and complete earlier analytical and numerical studies.The T = 0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metast

Modelling Avalanches in Martensites

“…The existence of such peak suggests that the stability limit of equilibrium branches for the RSSM has a reentrant behaviour in the space (ē, σ). This behaviour is similar to that observed in the magnetisation-driven RFIM [117,118] and is reminiscent of the re-entrant behaviour of the boundaries of the region of typical [119] states reported for the RFIM [120,121].…”

A universal form of slow dynamics in zero-temperature random-field Ising model

“…Thus far, several interesting results on the quasi-static properties of the model on Bethe lattices have been obtained [14,15,16,17,18,19,20]. In this Letter, by performing the bifurcation analysis of the derived equation, we determine the critical exponents characterizing singular behaviors of dynamical processes.…”

Clock Monte Carlo methods

“…The normalization is c(N ) = 1/N , and the system belongs to the class of strict extensivity. Random-field models have applications in a wide range of physics [45][46][47][48][49], including the pinning of vortices in superconductors, Coulomb glass, the metal-insulator transition, and hysteresis and avalanche physics. In general spatial dimensions, the thermodynamic properties and phase transitions are still debated [50,51].…”