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 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 a striped structure, in contrast to common expectations. The universal relationship between the critical percolation and the probability of a striped 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.