Abstract
We investigate the dynamical fixed points of the zero temperature Glauber dynamics in Ising-like models. The stability analysis of the fixed points in the mean field calculation shows the existence of an exponent that depends on the coordination number in the Ising model. For the generalized voter model, a phase diagram is obtained based on this study. Numerical results for the Ising model for both the mean field case and short ranged models on lattices with different values of are also obtained. A related study is the behavior of the exit probability , defined as the probability that a configuration ends up with all spins up starting with fraction of up spins. An interesting result is in the mean field approximation when , which is consistent with the conserved magnetization in the system. For larger values of shows the usual finite size dependent nonlinear behavior both in the mean field model and in the Ising model with nearest neighbor interaction on different two dimensional lattices. For such a behavior, a data collapse of is obtained using as the scaling variable and appears as the scaling function. The universality of the exponent and the scaling factor is investigated.
7 More- Received 13 July 2021
- Revised 14 August 2021
- Accepted 31 August 2021
DOI:https://doi.org/10.1103/PhysRevE.104.034123
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