---
_id: '2300'
abstract:
- lang: eng
  text: We consider Ising models in two and three dimensions with nearest neighbor
    ferromagnetic interactions and long-range, power law decaying, antiferromagnetic
    interactions. If the strength of the ferromagnetic coupling J is larger than a
    critical value Jc, then the ground state is homogeneous and ferromagnetic. As
    the critical value is approached from smaller values of J, it is believed that
    the ground state consists of a periodic array of stripes (d=2) or slabs (d=3),
    all of the same size and alternating magnetization. Here we prove rigorously that
    the ground state energy per site converges to that of the optimal periodic striped
    or slabbed state, in the limit that J tends to the ferromagnetic transition point.
    While this theorem does not prove rigorously that the ground state is precisely
    striped or slabbed, it does prove that in any suitably large box the ground state
    is striped or slabbed with high probability.
article_number: '064401'
article_processing_charge: No
arxiv: 1
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. Realization of stripes and slabs in two and
    three dimensions. <i>Physical Review B</i>. 2013;88(6). doi:<a href="https://doi.org/10.1103/PhysRevB.88.064401">10.1103/PhysRevB.88.064401</a>
  apa: Giuliani, A., Lieb, É., &#38; Seiringer, R. (2013). Realization of stripes
    and slabs in two and three dimensions. <i>Physical Review B</i>. American Physical
    Society. <a href="https://doi.org/10.1103/PhysRevB.88.064401">https://doi.org/10.1103/PhysRevB.88.064401</a>
  chicago: Giuliani, Alessandro, Élliott Lieb, and Robert Seiringer. “Realization
    of Stripes and Slabs in Two and Three Dimensions.” <i>Physical Review B</i>. American
    Physical Society, 2013. <a href="https://doi.org/10.1103/PhysRevB.88.064401">https://doi.org/10.1103/PhysRevB.88.064401</a>.
  ieee: A. Giuliani, É. Lieb, and R. Seiringer, “Realization of stripes and slabs
    in two and three dimensions,” <i>Physical Review B</i>, vol. 88, no. 6. American
    Physical Society, 2013.
  ista: Giuliani A, Lieb É, Seiringer R. 2013. Realization of stripes and slabs in
    two and three dimensions. Physical Review B. 88(6), 064401.
  mla: Giuliani, Alessandro, et al. “Realization of Stripes and Slabs in Two and Three
    Dimensions.” <i>Physical Review B</i>, vol. 88, no. 6, 064401, American Physical
    Society, 2013, doi:<a href="https://doi.org/10.1103/PhysRevB.88.064401">10.1103/PhysRevB.88.064401</a>.
  short: A. Giuliani, É. Lieb, R. Seiringer, Physical Review B 88 (2013).
date_created: 2018-12-11T11:56:51Z
date_published: 2013-08-01T00:00:00Z
date_updated: 2025-09-29T14:18:13Z
day: '01'
department:
- _id: RoSe
doi: 10.1103/PhysRevB.88.064401
external_id:
  arxiv:
  - '1305.5323'
  isi:
  - '000322721000002'
intvolume: '        88'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1305.5323
month: '08'
oa: 1
oa_version: Preprint
publication: Physical Review B
publication_status: published
publisher: American Physical Society
publist_id: '4627'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Realization of stripes and slabs in two and three dimensions
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 88
year: '2013'
...
---
_id: '2318'
abstract:
- lang: eng
  text: 'We show that bosons interacting via pair potentials with negative scattering
    length form bound states for a suitable number of particles. In other words, the
    absence of many-particle bound states of any kind implies the non-negativity of
    the scattering length of the interaction potential. '
acknowledgement: 'Partial financial support by NSERC '
article_processing_charge: No
arxiv: 1
author:
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Seiringer R. Absence of bound states implies non-negativity of the scattering
    length. <i>Journal of Spectral Theory</i>. 2012;2(3):321-328. doi:<a href="https://doi.org/10.4171/JST/31">10.4171/JST/31</a>
  apa: Seiringer, R. (2012). Absence of bound states implies non-negativity of the
    scattering length. <i>Journal of Spectral Theory</i>. European Mathematical Society.
    <a href="https://doi.org/10.4171/JST/31">https://doi.org/10.4171/JST/31</a>
  chicago: Seiringer, Robert. “Absence of Bound States Implies Non-Negativity of the
    Scattering Length.” <i>Journal of Spectral Theory</i>. European Mathematical Society,
    2012. <a href="https://doi.org/10.4171/JST/31">https://doi.org/10.4171/JST/31</a>.
  ieee: R. Seiringer, “Absence of bound states implies non-negativity of the scattering
    length,” <i>Journal of Spectral Theory</i>, vol. 2, no. 3. European Mathematical
    Society, pp. 321–328, 2012.
  ista: Seiringer R. 2012. Absence of bound states implies non-negativity of the scattering
    length. Journal of Spectral Theory. 2(3), 321–328.
  mla: Seiringer, Robert. “Absence of Bound States Implies Non-Negativity of the Scattering
    Length.” <i>Journal of Spectral Theory</i>, vol. 2, no. 3, European Mathematical
    Society, 2012, pp. 321–28, doi:<a href="https://doi.org/10.4171/JST/31">10.4171/JST/31</a>.
  short: R. Seiringer, Journal of Spectral Theory 2 (2012) 321–328.
corr_author: '1'
date_created: 2018-12-11T11:56:58Z
date_published: 2012-06-24T00:00:00Z
date_updated: 2025-09-30T08:22:10Z
day: '24'
department:
- _id: RoSe
doi: 10.4171/JST/31
external_id:
  arxiv:
  - '1204.0435'
  isi:
  - '000209021900004'
intvolume: '         2'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1204.0435
month: '06'
oa: 1
oa_version: Preprint
page: 321-328
publication: Journal of Spectral Theory
publication_status: published
publisher: European Mathematical Society
publist_id: '4609'
quality_controlled: '1'
status: public
title: Absence of bound states implies non-negativity of the scattering length
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 2
year: '2012'
...