We consider zero-temperature, stochastic Ising models σt 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 σt 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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)