1995/07/01 by Satya N. Majumdar, David A. Huse · 2 citations
Materials Science · Mathematics · Physics and Astronomy · #Block Copolymer Self-Assembly #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · doi:10.1103/physreve.52.270
openalex publication_date 1995/07/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We present a general framework for the time-dependent correlation functions in a phase-ordering system after a quench from the disordered phase to or below the critical point and discuss under what conditions the two-time exponents \ensuremathλ or \ensuremathλc [characterizing the decay of local autocorrelations, 〈\ensuremathφ(r\ensuremath→,0)\ensuremathφ(r\ensuremath→,t)〉\ensuremath∼L^\mathrm\ensuremath-\ensuremathλ or \ensuremath∼Lc^\mathrm\ensuremath-\ensuremathλ for quenches to below Tc or to Tc, respectively, where L(t) is the correlation length at time t, and \ensuremathφ is the order parameter] are equal to the spatial dimension d in the conserved order parameter case. We present a few cases where exact solutions and numerical simulations suggest \ensuremathλc=d. The same, however, is not true for the exponent \ensuremathλ. We present one example, namely a deterministic conserved model in one dimension, where \ensuremathλ is explicitly less than d=1. This led us to study the differences and similarities between stochastic and deterministic models of coarsening. In this paper, we address this general issue with a focus in one dimension, where the two classes of models are discussed in parallel and several analytical and numerical results are derived.