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
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.
