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

TL;DR

This study explores how zero-temperature Glauber dynamics influence the long-term states of Ising ferromagnets and antiferromagnets on various two-dimensional lattices, revealing new types of states and relationships with percolation.

Contribution

It uncovers the existence of blinker states in even-coordinated lattices and establishes a universal link between percolation and stripe formation probabilities.

Findings

Blinker states are observed alongside ground and metastable states.

Even-coordinated lattices can reach blinker or metastable states without stripe structures.

A universal relationship between percolation and stripe final states is confirmed.

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.