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In the past decade low-temperature Glauber dynamics for the one-dimensionalIsing system has been several times observed experimentally and occurred to beone of the most important theoretical approaches in a field of molecularnanomagnets. On the other hand, it has been shown recently that Glauberdynamics with the Metropolis flipping probability for the zero-temperatureIsing ferromagnet under synchronous updating can lead surprisingly to theantiferromagnetic steady state. In this paper the generalized class of Glauberdynamics at zero-temperature will be considered and the relaxation into theground state, after a quench from high temperature, will be investigated. UsingMonte Carlo simulations and a mean field approach, discontinuous phasetransition between ferromagnetic and antiferromagnetic phases for aone-dimensional ferromagnet will be shown.

Phase transition in a one-dimensional Ising ferromagnet at zero-temperature under Glauber dynamics with a synchronous updating mode