Scaling and Crossover in the Large-N Model for Growth Kinetics

TL;DR

This paper investigates the scaling behaviors in growth kinetics using a large-N model, revealing diverse asymptotic regimes, fixed point structures, and crossover phenomena influenced by system parameters and conservation laws.

Contribution

It provides a comprehensive analysis of how scaling properties depend on dimensionality, interaction range, and conservation laws within the large-N growth model, including explicit crossover mechanisms.

Findings

Rich variety of asymptotic behaviors including standard scaling and multiscaling

Identification of fixed points controlling different scaling regimes

Explicit description of crossover phenomena between regimes

Abstract

The dependence of the scaling properties of the structure factor on space dimensionality, range of interaction, initial and final conditions, presence or absence of a conservation law is analysed in the framework of the large-N model for growth kinetics. The variety of asymptotic behaviours is quite rich, including standard scaling, multiscaling and a mixture of the two. The different scaling properties obtained as the parameters are varied are controlled by a structure of fixed points with their domains of attraction. Crossovers arising from the competition between distinct fixed points are explicitely obtained. Temperature fluctuations below the critical temperature are not found to be irrelevant when the order parameter is conserved. The model is solved by integration of the equation of motion for the structure factor and by a renormalization group approach.