Field-induced freezing in the unfrustrated Ising antiferromagnet

We study instantaneous quenches from infinite temperature to well below T_c in the two-dimensional (2D) square lattice Ising antiferromagnet in the presence of a longitudinal external magnetic field. Under single-spin-flip Metropolis algorithm Monte Carlo dynamics, this protocol produces a pair of metastable magnetization plateaus that prevent the system from reaching the equilibrium ground state except for some special values of the field. This occurs despite the absence of intrinsic disorder or frustration. We explain the plateaus in terms of local spin configurations that are stable under the dynamics. Although the details of the plateaus depend on the update scheme, the underlying principle governing the breakdown of ergodicity is quite general and provides a broader paradigm for understanding failures of ergodicity in Monte Carlo dynamics. See also: Iaizzi, Phys. Rev. E 102 032112 (2020), doi: 10.1103/PhysRevE.102.032112