# Periodic striped states in Ising models with dipolar interactions

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)

Keywords:

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