{"volume":331,"article_type":"original","has_accepted_license":"1","external_id":{"arxiv":["1304.6344"]},"day":"01","quality_controlled":"1","date_updated":"2022-05-24T08:32:50Z","intvolume":"       331","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 &gt; 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."}],"status":"public","acknowledgement":"2014 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.\r\n\r\nThe research leading to these results has received funding from the European Research\r\nCouncil under the European Union’s Seventh Framework Programme ERC Starting Grant CoMBoS (Grant Agreement No. 239694; A.G. and R.S.), the U.S. National Science Foundation (Grant PHY 0965859; E.H.L.), the Simons Foundation (Grant # 230207; E.H.L) and the NSERC (R.S.). The work is part of a project started in collaboration with Joel Lebowitz, whom we thank for many useful discussions and for his constant encouragement.","publication_status":"published","scopus_import":"1","oa":1,"publisher":"Springer","oa_version":"Published Version","citation":{"apa":"Giuliani, A., Lieb, É., &#38; Seiringer, R. (2014). Formation of stripes and slabs near the ferromagnetic transition. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-014-1923-2\">https://doi.org/10.1007/s00220-014-1923-2</a>","short":"A. Giuliani, É. Lieb, R. Seiringer, Communications in Mathematical Physics 331 (2014) 333–350.","mla":"Giuliani, Alessandro, et al. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” <i>Communications in Mathematical Physics</i>, vol. 331, Springer, 2014, pp. 333–50, doi:<a href=\"https://doi.org/10.1007/s00220-014-1923-2\">10.1007/s00220-014-1923-2</a>.","ieee":"A. Giuliani, É. Lieb, and R. Seiringer, “Formation of stripes and slabs near the ferromagnetic transition,” <i>Communications in Mathematical Physics</i>, vol. 331. Springer, pp. 333–350, 2014.","chicago":"Giuliani, Alessandro, Élliott Lieb, and Robert Seiringer. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” <i>Communications in Mathematical Physics</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s00220-014-1923-2\">https://doi.org/10.1007/s00220-014-1923-2</a>.","ama":"Giuliani A, Lieb É, Seiringer R. Formation of stripes and slabs near the ferromagnetic transition. <i>Communications in Mathematical Physics</i>. 2014;331:333-350. doi:<a href=\"https://doi.org/10.1007/s00220-014-1923-2\">10.1007/s00220-014-1923-2</a>","ista":"Giuliani A, Lieb É, Seiringer R. 2014. Formation of stripes and slabs near the ferromagnetic transition. Communications in Mathematical Physics. 331, 333–350."},"type":"journal_article","doi":"10.1007/s00220-014-1923-2","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"_id":"1935","month":"10","title":"Formation of stripes and slabs near the ferromagnetic transition","year":"2014","file":[{"relation":"main_file","file_size":334064,"date_created":"2022-05-24T08:30:40Z","file_name":"2014_CommMathPhysics_Giuliani.pdf","content_type":"application/pdf","date_updated":"2022-05-24T08:30:40Z","creator":"dernst","checksum":"c8423271cd1e1ba9e44c47af75efe7b6","file_id":"11409","access_level":"open_access","success":1}],"ddc":["510"],"date_published":"2014-10-01T00:00:00Z","article_processing_charge":"No","publication":"Communications in Mathematical Physics","date_created":"2018-12-11T11:54:48Z","page":"333 - 350","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"RoSe"}],"language":[{"iso":"eng"}],"file_date_updated":"2022-05-24T08:30:40Z","publist_id":"5159","author":[{"last_name":"Giuliani","first_name":"Alessandro","full_name":"Giuliani, Alessandro"},{"first_name":"Élliott","full_name":"Lieb, Élliott","last_name":"Lieb"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert"}]}