Fixation for Zero-Temperature Stochastic Ising Models on the Hexagonal Lattice
نویسندگان
چکیده
We investigate zero-temperature dynamics on the hexagonal lattice H for the homogeneous ferromagnetic Ising model with zero external magnetic field and a disordered ferromagnetic Ising model with a positive external magnetic field h. We consider both continuous time (asynchronous) processes and, in the homogeneous case, also discrete time synchronous dynamics (i.e., a deterministic cellular automaton), alternating between two sublattices of H. The state space consists of assignments of −1 or +1 to each site of H, and the processes are zero-temperature limits of stochastic Ising ferromagnets with Glauber dynamics and a random (i.i.d. Bernoulli) spin configuration at time 0. We study the speed of convergence of the configuration σt at time t to its limit σ∞ and related issues. Mathematics Subject Classification 2000: 60K35, 82C22, 60K37, 37B15, 82C20.
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تاریخ انتشار 2002