Establish the mechanism of hysteresis and rare simulation jumps

Establish whether the proposed population-annealing mechanism involving rare low-energy configurations without vertically percolating stripes accounts for the hysteresis and sudden jumps observed in simulations of the J1-J2 Ising model on the honeycomb lattice at J2 = −1.

Background

At J2 = −1, low-temperature specific-heat features and hysteresis appear in heating and cooling simulations, but equilibration is unreliable. The authors propose that rare replicas lacking vertical stripes may have lower energy and can take over the population during cooling, while heating begins from states without such stripes. This mechanism is explicitly presented as a conjecture and remains to be tested with methods better suited to first-order-like behavior.