A Mermin–Wagner Theorem for Gibbs States on Lorentzian Triangulations
| Autor: | Anatoly Yambartsev, Yu. M. Suhov, Mark Kelbert |
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| Rok vydání: | 2013 |
| Předmět: |
Physics
Dimension (graph theory) FOS: Physical sciences Statistical and Nonlinear Physics Torus Mathematical Physics (math-ph) Type (model theory) TOPOLOGIA DIFERENCIAL Tree (descriptive set theory) symbols.namesake Mermin–Wagner theorem Distribution (mathematics) symbols 60F05 60J60 60J80 Invariant (mathematics) Gibbs measure Mathematical Physics Mathematical physics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| ISSN: | 1572-9613 0022-4715 |
| DOI: | 10.1007/s10955-013-0698-8 |
| Popis: | We establish a Mermin--Wagner type theorem for Gibbs states on infinite random Lorentzian triangulations (LT) arising in models of quantum gravity. Such a triangulation is naturally related to the distribution $\sf P$ of a critical Galton--Watson tree, conditional upon non-extinction. At the vertices of the triangles we place classical spins taking values in a torus $M$ of dimension $d$, with a given group action of a torus ${\tt G}$ of dimension $d'\leq d$. In the main body of the paper we assume that the spins interact via a two-body nearest-neighbor potential $U(x,y)$ invariant under the action of ${\tt G}$. We analyze quenched Gibbs measures generated by $U$ and prove that, for $\sf P$-almost all Lorentzian triangulations, every such Gibbs measure is ${\tt G}$-invariant, which means the absence of spontaneous continuous symmetry-breaking. Comment: 10n pages, 1 figure |
| Databáze: | OpenAIRE |
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