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

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.

48 pages with 6 figures available upon request, plain LaTex

Cited by in corpus (34)

• Theory of Phase Ordering Kinetics
• Phenomenology of local scale invariance: from conformal invariance to dynamical scaling
• Two-scale competition in phase separation with shear
• Spinodal decomposition of a binary mixture in an uniform shear flow
• Scaling and hydrodynamic effects in lamellar ordering
• Scaling of the linear response function from zero field cooled and thermoremanent magnetization in phase ordering kinetics
• Lamellar order, microphase structures and glassy phase in a field theoretic model for charged colloids
• Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?
• Phase-separation of binary fluids in shear flow: a numerical study
• Structure and rheology of binary mixtures in shear flow
• Condensation vs. phase-ordering in the dynamics of first order transitions
• Early stage scaling in phase ordering kinetics
• Spherical model of growing interfaces
• Phase-Ordering Dynamics with an Order-Parameter-Dependent Mobility: The Large-n Limit
• Correlation Functions and Fluctuation-Dissipation Relation in Driven Mixtures: an exactly solvable model
• Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench
• The kinetic spherical model in a magnetic field
• Energy and Heat Fluctuations in a Temperature Quench
• Lindblad dynamics of the quantum spherical model
• Axiomatic construction of quantum Langevin equations
• The role of initial state and final quench temperature on the aging properties in phase-ordering kinetics
• Off-equilibrium dynamics in a singular diffusion model
• Overall time evolution in phase-ordering kinetics
• Coarsening and Pinning in the Self-consistent Solution of Polymer Blends Phase-Separation Kinetics
• Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing
• Diffusion Limited Growth in Systems with Continuous Symmetry
• The Effect of Shear on Phase-Ordering Dynamics with Order-Parameter-Dependent Mobility: The Large-n Limit
• A Soluble Phase Field Model
• Phase-ordering of conserved vectorial systems with field-dependent mobility
• Growth Kinetics in a Phase Field Model with Continuous Symmetry
• Preasymptotic multiscaling in the phase-ordering dynamics of the kinetic Ising model
• Studying nonlinear effects on the early stage of phase ordering using a decomposition method
• Dynamics of Cosmological Phase Transitions: What Can We Learn from Condensed Matter Physics?
• Self tuning phase separation in a model with competing interactions inspired by biological cell polarization