Non-Backtracking Loop Soups and Statistical Mechanics on Spin Networks

Federico Camia, Marcin Lis

    Research output: Contribution to journalArticle

    Abstract

    We introduce and study a Markov field on the edges of a graph G in dimension d≥ 2 whose configurations are spin networks. The field arises naturally as the edge-occupation field of a Poissonian model (a soup) of non-backtracking loops and walks characterized by a spatial Markov property such that, conditionally on the value of the edge-occupation field on a boundary set that splits the graph into two parts, the distributions of the loops and arcs contained in the two parts are independent of each other. The field has a Gibbs distribution with a Hamiltonian given by a sum of terms which involve only edges incident on the same vertex. Its free energy density and other quantities can be computed exactly, and their critical behavior analyzed, in any dimension.

    Original languageEnglish (US)
    Pages (from-to)403-433
    Number of pages31
    JournalAnnales Henri Poincare
    Volume18
    Issue number2
    DOIs
    StatePublished - Feb 1 2017

    Fingerprint

    statistical mechanics
    Statistical Mechanics
    occupation
    Gibbs Distribution
    Markov Property
    Graph in graph theory
    Critical Behavior
    apexes
    Energy Density
    flux density
    arcs
    Walk
    free energy
    Free Energy
    Arc of a curve
    configurations
    Configuration
    Term
    Vertex of a graph

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Nuclear and High Energy Physics
    • Mathematical Physics

    Cite this

    Non-Backtracking Loop Soups and Statistical Mechanics on Spin Networks. / Camia, Federico; Lis, Marcin.

    In: Annales Henri Poincare, Vol. 18, No. 2, 01.02.2017, p. 403-433.

    Research output: Contribution to journalArticle

    Camia, Federico ; Lis, Marcin. / Non-Backtracking Loop Soups and Statistical Mechanics on Spin Networks. In: Annales Henri Poincare. 2017 ; Vol. 18, No. 2. pp. 403-433.
    @article{b03984b25480428a9d7ce04963c13585,
    title = "Non-Backtracking Loop Soups and Statistical Mechanics on Spin Networks",
    abstract = "We introduce and study a Markov field on the edges of a graph G in dimension d≥ 2 whose configurations are spin networks. The field arises naturally as the edge-occupation field of a Poissonian model (a soup) of non-backtracking loops and walks characterized by a spatial Markov property such that, conditionally on the value of the edge-occupation field on a boundary set that splits the graph into two parts, the distributions of the loops and arcs contained in the two parts are independent of each other. The field has a Gibbs distribution with a Hamiltonian given by a sum of terms which involve only edges incident on the same vertex. Its free energy density and other quantities can be computed exactly, and their critical behavior analyzed, in any dimension.",
    author = "Federico Camia and Marcin Lis",
    year = "2017",
    month = "2",
    day = "1",
    doi = "10.1007/s00023-016-0524-3",
    language = "English (US)",
    volume = "18",
    pages = "403--433",
    journal = "Annales Henri Poincare",
    issn = "1424-0637",
    publisher = "Birkhauser Verlag Basel",
    number = "2",

    }

    TY - JOUR

    T1 - Non-Backtracking Loop Soups and Statistical Mechanics on Spin Networks

    AU - Camia, Federico

    AU - Lis, Marcin

    PY - 2017/2/1

    Y1 - 2017/2/1

    N2 - We introduce and study a Markov field on the edges of a graph G in dimension d≥ 2 whose configurations are spin networks. The field arises naturally as the edge-occupation field of a Poissonian model (a soup) of non-backtracking loops and walks characterized by a spatial Markov property such that, conditionally on the value of the edge-occupation field on a boundary set that splits the graph into two parts, the distributions of the loops and arcs contained in the two parts are independent of each other. The field has a Gibbs distribution with a Hamiltonian given by a sum of terms which involve only edges incident on the same vertex. Its free energy density and other quantities can be computed exactly, and their critical behavior analyzed, in any dimension.

    AB - We introduce and study a Markov field on the edges of a graph G in dimension d≥ 2 whose configurations are spin networks. The field arises naturally as the edge-occupation field of a Poissonian model (a soup) of non-backtracking loops and walks characterized by a spatial Markov property such that, conditionally on the value of the edge-occupation field on a boundary set that splits the graph into two parts, the distributions of the loops and arcs contained in the two parts are independent of each other. The field has a Gibbs distribution with a Hamiltonian given by a sum of terms which involve only edges incident on the same vertex. Its free energy density and other quantities can be computed exactly, and their critical behavior analyzed, in any dimension.

    UR - http://www.scopus.com/inward/record.url?scp=84991786896&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84991786896&partnerID=8YFLogxK

    U2 - 10.1007/s00023-016-0524-3

    DO - 10.1007/s00023-016-0524-3

    M3 - Article

    VL - 18

    SP - 403

    EP - 433

    JO - Annales Henri Poincare

    JF - Annales Henri Poincare

    SN - 1424-0637

    IS - 2

    ER -