Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Abstract

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model, Φ= −|a/2|m²+|b/4|m⁴- mh(t) , to study hysteresis effects. The field is swept at a constant rate h(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimum m(0) are recorded, on passage to a global minimum m( τ). The results are: (a) The mean jump h̅_J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time < τ > (FPT); (b) The broad jump distribution ρ(h_J,h) is related to intrinsically large FPT fluctuations (< τ² > - < τ > ²)/ < τ² > ~ O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.