{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/permutation-glass","title":"Permutation glass","arxiv_id":"1801.03231","date":"2018-01-10","proceeding":null,"authors":["Mobolaji Williams"],"abstract":"The field of disordered systems provides many simple models in which the competing influences of thermal and non-thermal disorder lead to new phases and non-trivial thermal behavior of order parameters. In this paper, we add a model to the subject by considering a system where the state space consists of various orderings of a list. As in spin glasses, the disorder of such \"permutation glasses\" arises from a parameter in the Hamiltonian being drawn from a distribution of possible values, thus allowing nominally \"incorrect orderings\" to have lower energies than \"correct orderings\" in the space of permutations. We analyze a Gaussian, uniform, and symmetric Bernoulli distribution of energy costs, and, by employing Jensen's inequality, derive a general condition requiring the permutation glass to always transition to the correctly ordered state at a temperature lower than that of the non-disordered system, provided that this correctly ordered state is accessible. We in turn find that in order for the correctly ordered state to be accessible, the probability that an incorrectly-ordered component is energetically favored must be less than the inverse of the number of components in the system. We show that all of these results are consistent with a replica symmetric ansatz of the system and argue that there is no permutation glass phase characterized by replica symmetry breaking, but there is glassy behavior represented by a residual entropy at zero temperature. We conclude by discussing an apparent duality between permutation glasses and fermion gases.","url_abs":"http://arxiv.org/abs/1801.03231v3","url_pdf":"http://arxiv.org/pdf/1801.03231v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"permutation-glass","repo_url":"https://github.com/mowillia/PermutationGlass","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}