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|m ²+|b/4|m ⁴−mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(τ). The results are: (a) The mean jump¯h _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 distributionρ(h _J,h) is related to intrinsically large FPT fluctuations (〈τ ²〉−〈τ〉²)/〈τ ²〉 ∼ O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.