FM 11-15; arXiv:1509.00057

Authors: Alessandro Giuliani, Robert Seiringer

Title: Periodic striped ground states in Ising models with competing interactions

Abstract: We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d+1, with d the space dimension, this happens for all values of J smaller than a critical value Jc(p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p>2d and J in a left neighborhood of Jc(p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (d=2) or slabs (d=3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.

Alessandro Giuliani
Dipartimento di Matematica e Fisica
Università degli Studi Roma Tre
L.go S.L. Murialdo 1, 00146 Roma - Italy

Robert Seiringer
Institute of Science and Technology Austria (IST Austria)
Am Campus 1
A - 3400 Klosterneuburg