Condensation vs. phase-ordering in the dynamics of first order transitions

TL;DR

This paper investigates the non-commutativity of limits in the dynamics of first order transitions, revealing different behaviors depending on the order of limits and analyzing scaling properties in the large-N model.

Contribution

It provides a detailed analysis of the scaling properties and crossover phenomena in the large-N model during first order transitions, highlighting differences in phase behavior.

Findings

Condensation of large wavelength fluctuations dominates when N→∞ first.

Preasymptotic scaling and crossover phenomena are identified.

Implications for realistic phase-ordering systems are discussed.

Abstract

The origin of the non commutativity of the limits $t \to \infty$ and $N \to \infty$ in the dynamics of first order transitions is investigated. In the large-N model, i.e. $N \to \infty$ taken first, the low temperature phase is characterized by condensation of the large wave length fluctuations rather than by genuine phase-ordering as when $t \to \infty$ is taken first. A detailed study of the scaling properties of the structure factor in the large-N model is carried out for quenches above, at and below T_c. Preasymptotic scaling is found and crossover phenomena are related to the existence of components in the order parameter with different scaling properties. Implications for phase-ordering in realistic systems are discussed.