Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 12 min ago
PreprintarXiv licencearXiv

Bootstrapping Classical Systems with Quenched Disorder

  • Minjae Cho
  • Yaprak Önder
  • Eslam Khalaf
  • Michael G. Scheer
Open at sourcePDFDOICite

Abstract

We introduce a bootstrap method for deriving bounds on disorder-averaged observables in classical statistical systems with quenched disorder. The three main ingredients of the bootstrap are the positivity of ensembles of probability measures, disorder-averaged equations of motion, and explicit expectation values of random coupling variables. Together, these ingredients lead to a linear programming problem over the space of disorder averages. By further employing the positivity of the two-replica Gram matrix, we also formulate a semidefinite programming problem that produces bounds on two-replica correlators. We demonstrate the method using two examples: the two-dimensional random site-diluted Ising model and the one-dimensional disordered contact process. For the latter example, the bootstrap bounds exhibit a region of multiple kinks that we relate to the Griffiths region, whose finite-size scaling analysis yields a typical correlation length exponent in good numerical agreement with the known value.

Related

  1. Universal sampling of spin systems across quenched disorder
    Jing Liu, Yeyuan Wu, Ying Tang +1
    arXivPreprintCC BY 4.0Full textCondensed matterStatistical & nonlinear physicsarXiv
  2. Bootstrapping Classical and Quantum Query Lower Bounds for Finding Tarski Fixed Points
    Tongyang Li, Weiran Ma, Ziyi Yang +1
    arXivPreprintarXiv licenceFull textQuantum physics & quantum informationarXiv
  3. Bootstrapping symmetries in quantum many-body systems from the cross spectral form factor
    Chen Bai, Zihan Zhou, Bastien Lapierre +1
    Physical Review XPeer-reviewedPublisher termsAtomic, molecular & optical physicsCrossref
  4. Two-stage Slowdown of Vacancy-mediated Diffusion in a Lattice Gas Model with Quenched Disorder and Spins
    Qiang Zhai
    arXivPreprintCC BY 4.0Full textCondensed matterarXiv
  5. Phase Diagram and Critical Behaviour of the Two-Dimensional Potts Model with Long-Range Quenched Disorder
    Rodolfo Rocha, Leticia F. Cugliandolo, Marco Picco
    arXivPreprintCC BY 4.0Full textCondensed matterStatistical & nonlinear physicsarXivHAL

Cite

BibTeXRIS
BibTeX
@misc{cho2026bootstrapping,
  title = {{Bootstrapping Classical Systems with Quenched Disorder}},
  author = {Minjae Cho and Yaprak Önder and Eslam Khalaf and Michael G. Scheer},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20927},
  eprint = {2609.20927},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20927},
}
RIS
TY  - UNPB
TI  - Bootstrapping Classical Systems with Quenched Disorder
AU  - Minjae Cho
AU  - Yaprak Önder
AU  - Eslam Khalaf
AU  - Michael G. Scheer
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20927
UR  - https://arxiv.org/abs/2609.20927
AB  - We introduce a bootstrap method for deriving bounds on disorder-averaged observables in classical statistical systems with quenched disorder. The three main ingredients of the bootstrap are the positivity of ensembles of probability measures, disorder-averaged equations of motion, and explicit expectation values of random coupling variables. Together, these ingredients lead to a linear programming problem over the space of disorder averages. By further employing the positivity of the two-replica Gram matrix, we also formulate a semidefinite programming problem that produces bounds on two-replica correlators. We demonstrate the method using two examples: the two-dimensional random site-diluted Ising model and the one-dimensional disordered contact process. For the latter example, the bootstrap bounds exhibit a region of multiple kinks that we relate to the Griffiths region, whose finite-size scaling analysis yields a typical correlation length exponent in good numerical agreement with the known value.
ER  -