Exact mapping of a spin glass with correlated disorder to the pure Ising model

[2602.22657] Exact mapping of a spin glass with correlated disorder to the pure Ising model Skip to main content Search Submit Donate Log in Condensed Matter > Disordered Systems and Neural Networks arXiv:2602.22657 (cond-mat) [Submitted on 26 Feb 2026 ( v1 ), last revised 15 May 2026 (this version, v2)] Title: Exact mapping of a spin glass with correlated disorder to the pure Ising model Authors: Hidetoshi Nishimori View PDF HTML (experimental) Abstract: We introduce an Ising spin-glass model with correlated disorder which continuously interpolates between the pure ferromagnetic Ising model and the Edwards-Anderson model with symmetric disorder. For this model, we prove that a Nishimori line (NL) can be defined, analogously to the Edwards-Anderson model, on which physical quantities can be expressed exactly in terms of those of the pure Ising model at a well-defined effective temperature on any lattice in any dimension. For example, the energy on the NL is equal to the energy of the pure Ising model at the effective temperature up to a constant and a trivial factor. More remarkably, the specific heat on the NL equals the energy, not the specific heat, of the pure Ising model at the effective temperature, again up to a constant and a trivial factor. Gauge-noninvariant quantities such as the magnetization and correlation functions are exactly equal to the corresponding quantities of the pure Ising model at the effective temperature. These exact relations imply that the leading critical behavior at that multicritical point for the disorder-correlated model is pure-Ising-like, in contrast to the conventional multicritical universality class of the standard Edwards-Anderson model. Our results motivate further investigations of the relatively unexplored topic of correlations in disorder in spin glasses and related problems. Comments: 910 pages Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn) Cite as: arXiv:2602.22657 [cond-mat.dis-nn] (or arXiv:2602.22657v2 [cond-mat.dis-nn] for this version) https://doi.org/10.48550/arXiv.2602.22657 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. E 113, 054124 (2026) Related DOI : https://doi.org/10.1103/99ls-2zdk Focus to learn more DOI(s) linking to related resources Submission history From: Hidetoshi Nishimori [ view email ] [v1] Thu, 26 Feb 2026 06:14:10 UTC (15 KB) [v2] Fri, 15 May 2026 23:18:57 UTC (428 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.dis-nn < prev | next > new | recent | 2026-02 Change to browse by: cond-mat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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