Updating schemes in zero-temperature single-spin flip dynamics

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In this paper we examine the role of the so called c-parallel updating schemes in relaxation from disordered states to the final ferromagnetic steady state. We investigate two zero-temperature single-spin flip dynamics on a one dimensional lattice of length L: inflow (i.e. generalized zero-temperature Glauber dynamics) and outflow opinion dynamics. The varying c allows us to change the updating scheme from random sequential updating (c=1/L) to deterministic synchronous updating (for c=1). We show how the mean relaxation times depend on c and scale with the system size L. Moreover, we empirically find an analytical formula for the ratio between mean relaxation times for inflow and outflow dynamics. Results obtained in this paper suggest that in some sense the original zero-temperature Glauber dynamics is a critical one among a broader class of inflow dynamics.