---
res:
bibo_abstract:
- '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.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Alessandro
foaf_name: Giuliani, Alessandro
foaf_surname: Giuliani
- foaf_Person:
foaf_givenName: Élliott
foaf_name: Lieb, Élliott
foaf_surname: Lieb
- foaf_Person:
foaf_givenName: Robert
foaf_name: Seiringer, Robert
foaf_surname: Seiringer
foaf_workInfoHomepage: http://www.librecat.org/personId=4AFD0470-F248-11E8-B48F-1D18A9856A87
bibo_doi: 10.1007/s00220-014-1923-2
bibo_issue: '1'
bibo_volume: 331
dct_date: 2014^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: Formation of stripes and slabs near the ferromagnetic transition@
...