[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","dini_type":"doc-type:article","citation":{"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.","ista":"Giuliani A, Lieb É, Seiringer R. 2014. Formation of stripes and slabs near the ferromagnetic transition. Communications in Mathematical Physics. 331, 333–350.","mla":"Giuliani, Alessandro, et al. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” Communications in Mathematical Physics, vol. 331, Springer, 2014, pp. 333–50, doi:10.1007/s00220-014-1923-2.","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","ieee":"A. Giuliani, É. Lieb, and R. Seiringer, “Formation of stripes and slabs near the ferromagnetic transition,” Communications in Mathematical Physics, vol. 331. Springer, pp. 333–350, 2014.","short":"A. Giuliani, É. Lieb, R. Seiringer, Communications in Mathematical Physics 331 (2014) 333–350."},"external_id":{"arxiv":[]},"article_processing_charge":"No","author":[{"last_name":"Giuliani","first_name":"Alessandro"},{"first_name":"Élliott","last_name":"Lieb"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"publist_id":"5159","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.","oa":1,"quality_controlled":"1","publication":"Communications in Mathematical Physics","dc":{"rights":["info:eu-repo/semantics/openAccess"],"language":["eng"],"creator":["Giuliani, Alessandro","Lieb, Élliott","Seiringer, Robert"],"subject":["ddc:510"],"title":["Formation of stripes and slabs near the ferromagnetic transition"],"source":["Giuliani A, Lieb É, Seiringer R. Formation of stripes and slabs near the ferromagnetic transition. Communications in Mathematical Physics. 2014;331:333-350. doi:10.1007/s00220-014-1923-2"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1007/s00220-014-1923-2","info:eu-repo/semantics/altIdentifier/issn/0010-3616","info:eu-repo/semantics/altIdentifier/issn/1432-0916","info:eu-repo/semantics/altIdentifier/arxiv/1304.6344"],"identifier":["https://research-explorer.ista.ac.at/record/1935","https://research-explorer.ista.ac.at/download/1935/11409"],"description":["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."],"date":["2014"],"publisher":["Springer"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"]},"day":"01","has_accepted_license":"1","date_created":"2018-12-11T11:54:48Z","date_published":"2014-10-01T00:00:00Z","uri_base":"https://research-explorer.ista.ac.at","page":"333 - 350","_id":"1935","status":"public","type":"journal_article","article_type":"original","ddc":[],"creator":{"login":"apreinsp","id":"4435EBFC-F248-11E8-B48F-1D18A9856A87"},"date_updated":"2022-05-24T08:32:50Z","department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"RoSe"}],"file_date_updated":"2022-05-24T08:30:40Z","oa_version":"Published Version","abstract":[{"lang":"eng"}],"intvolume":" 331","month":"10","scopus_import":"1","language":[{}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"11409","checksum":"c8423271cd1e1ba9e44c47af75efe7b6","success":1,"creator":"dernst","date_updated":"2022-05-24T08:30:40Z","file_size":334064,"date_created":"2022-05-24T08:30:40Z","file_name":"2014_CommMathPhysics_Giuliani.pdf"}],"publication_status":"published","publication_identifier":{"issn":[],"eissn":[]},"volume":331}]