**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 J _{c}(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 J_{c}(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