Effective mobility and diffusivity in coarsening processes

¹ Dipartimento di Fisica “E. R. Caianiello”, and INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno - via Giovanni Paolo II 132, I-84084 Fisciano (SA), Italy
² Dipartimento di Matematica e Fisica, Università della Campania “L. Vanvitelli” - Viale Lincoln, Caserta, Italy
³ Istituto dei Sistemi Complessi, CNR - via Madonna del Piano 10, I-50019 Sesto Fiorentino (FI), Italy
⁴ INFN, Sezione di Firenze - via G. Sansone 1, I-50019, Sesto Fiorentino (FI), Italy

Received: 13 July 2017
Accepted: 8 September 2017

Abstract

We suggest that coarsening dynamics can be described in terms of a generalized random walk, with the dynamics of the growing length L(t) controlled by a drift term, , and a diffusive one, . We apply this interpretation to the one-dimensional Ising model with a ferromagnetic coupling constant decreasing exponentially on the scale R. In the case of non-conserved (Glauber) dynamics, both terms are present and their balance depends on the interplay between L(t) and R. In the case of conserved (Kawasaki) dynamics, drift is negligible, but is strongly dependent on L. The main pre-asymptotic regime displays a speeding of coarsening for Glauber dynamics and a slowdown for Kawasaki dynamics. We reason that a similar behaviour can be found in two dimensions.