---
_id: '43493'
abstract:
- lang: eng
  text: We consider a measure given as the continuum limit of a one-dimensional Ising
    model with long-range translationally invariant interactions. Mathematically,
    the measure can be described by a self-interacting Poisson driven jump process.
    We prove a correlation inequality, estimating the magnetic susceptibility of this
    model, which holds for small norm of the interaction function. The bound on the
    magnetic susceptibility has applications in quantum field theory and can be used
    to prove existence of ground states for the spin boson model.
article_type: original
author:
- first_name: David
  full_name: Hasler, David
  last_name: Hasler
- first_name: Benjamin
  full_name: Hinrichs, Benjamin
  id: '99427'
  last_name: Hinrichs
  orcid: 0000-0001-9074-1205
- first_name: Oliver
  full_name: Siebert, Oliver
  last_name: Siebert
citation:
  ama: Hasler D, Hinrichs B, Siebert O. Correlation bound for a one-dimensional continuous
    long-range Ising model. <i>Stochastic Processes and their Applications</i>. 2021;146:60-79.
    doi:<a href="https://doi.org/10.1016/j.spa.2021.12.010">10.1016/j.spa.2021.12.010</a>
  apa: Hasler, D., Hinrichs, B., &#38; Siebert, O. (2021). Correlation bound for a
    one-dimensional continuous long-range Ising model. <i>Stochastic Processes and
    Their Applications</i>, <i>146</i>, 60–79. <a href="https://doi.org/10.1016/j.spa.2021.12.010">https://doi.org/10.1016/j.spa.2021.12.010</a>
  bibtex: '@article{Hasler_Hinrichs_Siebert_2021, title={Correlation bound for a one-dimensional
    continuous long-range Ising model}, volume={146}, DOI={<a href="https://doi.org/10.1016/j.spa.2021.12.010">10.1016/j.spa.2021.12.010</a>},
    journal={Stochastic Processes and their Applications}, publisher={Elsevier BV},
    author={Hasler, David and Hinrichs, Benjamin and Siebert, Oliver}, year={2021},
    pages={60–79} }'
  chicago: 'Hasler, David, Benjamin Hinrichs, and Oliver Siebert. “Correlation Bound
    for a One-Dimensional Continuous Long-Range Ising Model.” <i>Stochastic Processes
    and Their Applications</i> 146 (2021): 60–79. <a href="https://doi.org/10.1016/j.spa.2021.12.010">https://doi.org/10.1016/j.spa.2021.12.010</a>.'
  ieee: 'D. Hasler, B. Hinrichs, and O. Siebert, “Correlation bound for a one-dimensional
    continuous long-range Ising model,” <i>Stochastic Processes and their Applications</i>,
    vol. 146, pp. 60–79, 2021, doi: <a href="https://doi.org/10.1016/j.spa.2021.12.010">10.1016/j.spa.2021.12.010</a>.'
  mla: Hasler, David, et al. “Correlation Bound for a One-Dimensional Continuous Long-Range
    Ising Model.” <i>Stochastic Processes and Their Applications</i>, vol. 146, Elsevier
    BV, 2021, pp. 60–79, doi:<a href="https://doi.org/10.1016/j.spa.2021.12.010">10.1016/j.spa.2021.12.010</a>.
  short: D. Hasler, B. Hinrichs, O. Siebert, Stochastic Processes and Their Applications
    146 (2021) 60–79.
date_created: 2023-04-14T04:50:01Z
date_updated: 2026-01-16T09:03:28Z
doi: 10.1016/j.spa.2021.12.010
extern: '1'
external_id:
  arxiv:
  - '2104.03013 '
intvolume: '       146'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
page: 60-79
publication: Stochastic Processes and their Applications
publication_identifier:
  issn:
  - 0304-4149
publication_status: published
publisher: Elsevier BV
status: public
title: Correlation bound for a one-dimensional continuous long-range Ising model
type: journal_article
user_id: '99427'
volume: 146
year: '2021'
...
---
_id: '43465'
abstract:
- lang: eng
  text: We show the existence of ground states in the massless spin boson model without
    any infrared regularization. Our proof is non-perturbative and relies on a compactness
    argument. It works for arbitrary values of the coupling constant under the hypothesis
    that the second derivative of the ground state energy as a function of a constant
    external magnetic field is bounded.
article_type: original
author:
- first_name: David
  full_name: Hasler, David
  last_name: Hasler
- first_name: Benjamin
  full_name: Hinrichs, Benjamin
  id: '99427'
  last_name: Hinrichs
  orcid: 0000-0001-9074-1205
- first_name: Oliver
  full_name: Siebert, Oliver
  last_name: Siebert
citation:
  ama: Hasler D, Hinrichs B, Siebert O. On Existence of Ground States in the Spin
    Boson Model. <i>Communications in Mathematical Physics</i>. 2021;388(1):419-433.
    doi:<a href="https://doi.org/10.1007/s00220-021-04185-w">10.1007/s00220-021-04185-w</a>
  apa: Hasler, D., Hinrichs, B., &#38; Siebert, O. (2021). On Existence of Ground
    States in the Spin Boson Model. <i>Communications in Mathematical Physics</i>,
    <i>388</i>(1), 419–433. <a href="https://doi.org/10.1007/s00220-021-04185-w">https://doi.org/10.1007/s00220-021-04185-w</a>
  bibtex: '@article{Hasler_Hinrichs_Siebert_2021, title={On Existence of Ground States
    in the Spin Boson Model}, volume={388}, DOI={<a href="https://doi.org/10.1007/s00220-021-04185-w">10.1007/s00220-021-04185-w</a>},
    number={1}, journal={Communications in Mathematical Physics}, publisher={Springer
    Science and Business Media LLC}, author={Hasler, David and Hinrichs, Benjamin
    and Siebert, Oliver}, year={2021}, pages={419–433} }'
  chicago: 'Hasler, David, Benjamin Hinrichs, and Oliver Siebert. “On Existence of
    Ground States in the Spin Boson Model.” <i>Communications in Mathematical Physics</i>
    388, no. 1 (2021): 419–33. <a href="https://doi.org/10.1007/s00220-021-04185-w">https://doi.org/10.1007/s00220-021-04185-w</a>.'
  ieee: 'D. Hasler, B. Hinrichs, and O. Siebert, “On Existence of Ground States in
    the Spin Boson Model,” <i>Communications in Mathematical Physics</i>, vol. 388,
    no. 1, pp. 419–433, 2021, doi: <a href="https://doi.org/10.1007/s00220-021-04185-w">10.1007/s00220-021-04185-w</a>.'
  mla: Hasler, David, et al. “On Existence of Ground States in the Spin Boson Model.”
    <i>Communications in Mathematical Physics</i>, vol. 388, no. 1, Springer Science
    and Business Media LLC, 2021, pp. 419–33, doi:<a href="https://doi.org/10.1007/s00220-021-04185-w">10.1007/s00220-021-04185-w</a>.
  short: D. Hasler, B. Hinrichs, O. Siebert, Communications in Mathematical Physics
    388 (2021) 419–433.
date_created: 2023-04-13T18:07:22Z
date_updated: 2026-01-16T09:02:44Z
doi: 10.1007/s00220-021-04185-w
extern: '1'
external_id:
  arxiv:
  - '2102.13373'
intvolume: '       388'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
oa: '1'
page: 419-433
publication: Communications in Mathematical Physics
publication_identifier:
  issn:
  - 0010-3616
  - 1432-0916
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: On Existence of Ground States in the Spin Boson Model
type: journal_article
user_id: '99427'
volume: 388
year: '2021'
...