[{"abstract":[{"lang":"eng","text":"We consider Ising models in d = 2 and d = 3 dimensions with nearest neighbor ferromagnetic and long-range antiferromagnetic interactions, the latter decaying as (distance)-p, p > 2d, at large distances. If the strength J of the ferromagnetic interaction is larger than a critical value J c, then the ground state is homogeneous. It has been conjectured that when J is smaller than but close to J c, the ground state is periodic and striped, with stripes of constant width h = h(J), and h → ∞ as J → Jc -. (In d = 3 stripes mean slabs, not columns.) Here we rigorously prove that, if we normalize the energy in such a way that the energy of the homogeneous state is zero, then the ratio e 0(J)/e S(J) tends to 1 as J → Jc -, with e S(J) being the energy per site of the optimal periodic striped/slabbed state and e 0(J) the actual ground state energy per site of the system. Our proof comes with explicit bounds on the difference e 0(J)-e S(J) at small but positive J c-J, and also shows that in this parameter range the ground state is striped/slabbed in a certain sense: namely, if one looks at a randomly chosen window, of suitable size ℓ (very large compared to the optimal stripe size h(J)), one finds a striped/slabbed state with high probability."}],"publist_id":"5159","oa_version":"Submitted Version","status":"public","author":[{"first_name":"Alessandro","last_name":"Giuliani","full_name":"Giuliani, Alessandro"},{"last_name":"Lieb","full_name":"Lieb, Élliott","first_name":"Élliott"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521"}],"language":[{"iso":"eng"}],"publisher":"Springer","month":"08","oa":1,"day":"01","publication":"Communications in Mathematical Physics","date_created":"2018-12-11T11:54:48Z","year":"2014","citation":{"mla":"Giuliani, Alessandro, et al. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” *Communications in Mathematical Physics*, vol. 331, no. 1, Springer, 2014, pp. 333–50, doi:10.1007/s00220-014-1923-2.","ama":"Giuliani A, Lieb É, Seiringer R. Formation of stripes and slabs near the ferromagnetic transition. *Communications in Mathematical Physics*. 2014;331(1):333-350. doi:10.1007/s00220-014-1923-2","ista":"Giuliani A, Lieb É, Seiringer R. 2014. Formation of stripes and slabs near the ferromagnetic transition. Communications in Mathematical Physics. 331(1), 333–350.","chicago":"Giuliani, Alessandro, Élliott Lieb, and Robert Seiringer. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” *Communications in Mathematical Physics*. Springer, 2014. https://doi.org/10.1007/s00220-014-1923-2.","short":"A. Giuliani, É. Lieb, R. Seiringer, Communications in Mathematical Physics 331 (2014) 333–350.","ieee":"A. Giuliani, É. Lieb, and R. Seiringer, “Formation of stripes and slabs near the ferromagnetic transition,” *Communications in Mathematical Physics*, vol. 331, no. 1. Springer, pp. 333–350, 2014.","apa":"Giuliani, A., Lieb, É., & Seiringer, R. (2014). Formation of stripes and slabs near the ferromagnetic transition. *Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-014-1923-2"},"publication_status":"published","issue":"1","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"1935","main_file_link":[{"url":"http://arxiv.org/abs/1304.6344","open_access":"1"}],"intvolume":" 331","doi":"10.1007/s00220-014-1923-2","page":"333 - 350","type":"journal_article","date_updated":"2021-01-12T06:54:11Z","scopus_import":1,"title":"Formation of stripes and slabs near the ferromagnetic transition","quality_controlled":"1","date_published":"2014-08-01T00:00:00Z","volume":331,"department":[{"_id":"RoSe"}]}]