---
_id: '1935'
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.'
author:
- first_name: Alessandro
full_name: Giuliani, Alessandro
last_name: Giuliani
- first_name: Élliott
full_name: Lieb, Élliott
last_name: Lieb
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
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
apa: Giuliani, A., Lieb, É., & Seiringer, R. (2014). Formation of stripes and
slabs near the ferromagnetic transition. *Communications in Mathematical Physics*,
*331*(1), 333–350. https://doi.org/10.1007/s00220-014-1923-2
chicago: 'Giuliani, Alessandro, Élliott Lieb, and Robert Seiringer. “Formation of
Stripes and Slabs near the Ferromagnetic Transition.” *Communications in Mathematical
Physics* 331, no. 1 (2014): 333–50. 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, no. 1, pp. 333–350, 2014.
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.
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.
short: A. Giuliani, É. Lieb, R. Seiringer, Communications in Mathematical Physics
331 (2014) 333–350.
date_created: 2018-12-11T11:54:48Z
date_published: 2014-08-01T00:00:00Z
date_updated: 2020-08-11T10:09:35Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00220-014-1923-2
intvolume: ' 331'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1304.6344
month: '08'
oa: 1
oa_version: Submitted Version
page: 333 - 350
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '5159'
quality_controlled: '1'
scopus_import: 1
status: public
title: Formation of stripes and slabs near the ferromagnetic transition
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 331
year: '2014'
...