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

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.

arXiv comment12 pages

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Cited by in corpus (11)

• Critical percolation in the dynamics of the 2d ferromagnetic Ising model
• Finite-Size Scaling Study of Aging during Coarsening in Non-Conserved Ising Model: The case of zero temperature quench
• Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals
• Percolation and coarsening in the bidimensional voter model
• Quench dynamics of the three-dimensional U(1) complex field theory: geometric and scaling characterisation of the vortex tangle
• Curvature-driven growth and interfacial noise in the voter model with self-induced zealots
• Dynamical cluster size heterogeneity
• Domain size heterogeneity in the Ising model: geometrical and thermal transitions
• Disentangling Growth and Decay of Domains During Phase Ordering
• Steady states and coarsening in one-dimensional driven Allen-Cahn system
• q-Gaussian Crossover in Overlap Spectra towards 3D Edwards-Anderson Criticality