Kinetics of phase-separation in the critical spherical model and local scale-invariance

TL;DR

This paper investigates the kinetics of phase separation in the critical spherical model, demonstrating that local scale-invariance accurately describes the scaling forms of correlation and response functions during the process.

Contribution

It provides an exact analysis of the critical spherical model's kinetics, confirming local scale-invariance as a symmetry and extending results to mass-conserving growth models.

Findings

Exact agreement with local scale-invariance predictions

Derivation of scaling forms for correlation and response functions

Application to mass-conserving kinetic growth models

Abstract

The scaling forms of the space- and time-dependent two-time correlation and response functions are calculated for the kinetic spherical model with a conserved order-parameter and quenched to its critical point from a completely disordered initial state. The stochastic Langevin equation can be split into a noise part and into a deterministic part which has local scale-transformations with a dynamical exponent z=4 as a dynamical symmetry. An exact reduction formula allows to express any physical average in terms of averages calculable from the deterministic part alone. The exact spherical model results are shown to agree with these predictions of local scale-invariance. The results also include kinetic growth with mass conservation as described by the Mullins-Herring equation.