Lifetime scaling for stripe metastable states under Z2-symmetric perturbations in the 2d Ising model

Prove that, for the two-dimensional Ising model initialized in a stripe metastable state and subjected to perturbations that preserve the Ising \mathbb{Z}_2 symmetry, the lifetime t_* scales as exp(c·ℓ²) in the stripe width ℓ. Establish this scaling rigorously by analyzing the resonant rectangle-flipping channel alone, in the absence of false-vacuum decay, starting from genuine metastable states where each stripe corresponds to a true ground state of the symmetric Hamiltonian.

Background

In the two-dimensional Ising setting studied in the paper, metastable stripe configurations are shown to have large metastability radii, and the authors rigorously bound lifetimes in the presence of generic perturbations. They further argue that when perturbations preserve the Ising \mathbb{Z}_2 symmetry, false-vacuum decay is absent; the dominant relaxation mechanism should then arise from processes that connect same-polarization stripes (e.g., flipping rectangles).

The authors explicitly state an expected scaling t_* ~ exp(Ω(ℓ²)) in this symmetric setting but note that they have not proved it. Establishing this scaling would sharpen the metastability theory in symmetric models and clarify the role of domain-wall dynamics in 2d.