Fate of Ising ferromagnets and antiferromagnets by zero-temperature Glauber dynamics on the two-dimensional Archimedean and 2-uniform lattices

Abstract

The fate of the Ising ferromagnet and antiferromagnet by the zero-temperature Glauber dynamics from random initial spin configuration is investigated in the two-dimensional Archimedean and 2-uniform lattices. Blinker states are found in addition to the ground state and metastable state. We show that an even-coordinated lattice can arrive at a blinker state or a metastable state without stripe structure, in contrast to common expectation. The universal relationship between the critical percolation and the probability of stripe final state is confirmed for six lattices. Results about the fate of the antiferromagnetic Ising model show that the geometric frustration suppresses ordering more and promotes blinker state.