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- W3103359698 abstract "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." @default.
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- W3103359698 date "2013-02-01" @default.
- W3103359698 modified "2023-09-25" @default.
- W3103359698 title "A Mermin–Wagner Theorem for Gibbs States on Lorentzian Triangulations" @default.
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- W3103359698 doi "https://doi.org/10.1007/s10955-013-0698-8" @default.
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