Zero-temperature dynamics of 2D and 3D Ising ferromagnets

We consider zero-temperature, stochastic Ising models σ^t with nearest-neighbour interactions in two and three dimensions. Using both symmetric and asymmetric initial configurations σ⁰, we study the evolution of the system with time. We examine the issue of convergence of σ^t and discuss the nature of the final state of the system. By determining a relation between the median number of spin flips per site ν, the probability p that a spin in the initial spin configuration takes the value +1, and lattice size L, we conclude that in two and three dimensions, the system converges to a frozen (but not necessarily uniform) state when p ≠ 1/2. Results for p = 1/2 in three dimensions are consistent with the conjecture that the system does not evolve towards a fully frozen limiting state. Our simulations also uncover 'striped' and 'blinker' states first discussed by Spirin et al (2001 Phys. Rev. E 63 036118), and their statistical properties are investigated.