Slicing the $3d$ Ising model: critical equilibrium and coarsening dynamics

TL;DR

This paper investigates the coarsening dynamics of 2D slices of the 3D Ising model after a quench, analyzing how domain structures evolve and confirming linear area decay with temperature-dependent prefactors.

Contribution

It provides a detailed analysis of the morphological evolution of spin clusters on 2D slices of the 3D Ising model, including the effects of initial conditions and temperature.

Findings

Area of initial configurations decays linearly over time.

Temperature influences the coarsening rate through a specific prefactor.

Morphological features of 2D slices resemble those of the 2D Ising model.

Abstract

We study the evolution of spin clusters on two dimensional slices of the $3d$ Ising model in contact with a heat bath after a sudden quench to a subcritical temperature. We analyze the evolution of some simple initial configurations, such as a sphere and a torus, of one phase embedded into the other, to confirm that their area disappears linearly in time and to establish the temperature dependence of the prefactor in each case. Two generic kinds of initial states are later used: equilibrium configurations either at infinite temperature or at the paramagnetic-ferromagnetic phase transition. We investigate the morphological domain structure of the coarsening configurations on $2d$ slices of the $3d$ system, comparing with the behavior of the bidimensional model.