We review the problem of determining the ground states of two-dimensional Ising models with nearest neighbor ferromagnetic and dipolar interactions, and prove a new result supporting the conjecture that, if the nearest neighbor coupling JJ 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.
Fermi, D., Giuliani, A. (2022). Periodic striped states in Ising models with dipolar interactions. In A.L. R.L. Frank (a cura di), The Physics and Mathematics of Elliott Lieb - The 90th Anniversary Volume I (pp. 269-293) [10.4171/90-1/12].
Periodic striped states in Ising models with dipolar interactions
D. Fermi
;A. Giuliani
2022-01-01
Abstract
We review the problem of determining the ground states of two-dimensional Ising models with nearest neighbor ferromagnetic and dipolar interactions, and prove a new result supporting the conjecture that, if the nearest neighbor coupling JJ 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
