Frozen into stripes: fate of the critical Ising model after a quench

TL;DR

This study numerically investigates the final states of the 2D critical Ising model after a zero-temperature quench, revealing the formation of stripe states linked to initial crossing probabilities and spanning cluster properties.

Contribution

It provides new insights into the relationship between initial crossing probabilities and the emergence of stripe states in the critical Ising model after a quench.

Findings

Stripe states are related to initial crossing probabilities.

Stripe states depend on properties of spanning clusters.

Results extend understanding beyond percolation to Ising model dynamics.

Abstract

In this work we study numerically the final state of the two dimensional ferromagnetic critical Ising model after a quench to zero temperature. Beginning from equilibrium at $T_c$, the system can be blocked in a variety of infinitely long lived stripe states in addition to the ground state. Similar results have already been obtained for an infinite temperature initial condition and an interesting connection to exact percolation crossing probabilities has emerged. Here we complete this picture by providing a new example of stripe states precisely related to initial crossing probabilities for various boundary conditions. We thus show that this is not specific to percolation but rather that it depends on the properties of spanning clusters in the initial state.