Davide Fermi, Alessandro Giuliani
March 02, 2022
We review the problem of determining the ground states of 2D Ising models with nearest neighbor ferromagnetic and dipolar interactions, and prove a new result supporting the conjecture that, if the nearest neighbor coupling $J$ is sufficiently large, the ground states are periodic and `striped'. More precisely, we prove a restricted version of the conjecture, by constructing the minimizers within the variational class of states whose domain walls are arbitrary collections of horizontal and/or vertical straight lines.
open access link pp. 269-293 in R. L.Frank, A. Laptev, M. Lewin, R. Seiringer (Eds.), ''The Physics and Mathematics of Elliott Lieb. The 90th Anniversary Volume I'', EMS Press (2022)