TY - JOUR

T1 - A Mermin-Wagner Theorem for Gibbs States on Lorentzian Triangulations

AU - Kelbert, M.

AU - Suhov, Yu

AU - Yambartsev, A.

N1 - Funding Information:
Acknowledgements This work was supported by FAPESP 2012/04372-7. M.K. thanks FAPESP 2011/ 20133-0 and thanks NUMEC for kind hospitality. The work of A.Y. was partially supported CNPq 308510/2010-0.

PY - 2013

Y1 - 2013

N2 - 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 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 G of dimension d′≤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 G. We analyze quenched Gibbs measures generated by U and prove that, for P-almost all Lorentzian triangulations, every such Gibbs measure is G-invariant, which means the absence of spontaneous continuous symmetry-breaking.

AB - 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 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 G of dimension d′≤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 G. We analyze quenched Gibbs measures generated by U and prove that, for P-almost all Lorentzian triangulations, every such Gibbs measure is G-invariant, which means the absence of spontaneous continuous symmetry-breaking.

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U2 - 10.1007/s10955-013-0698-8

DO - 10.1007/s10955-013-0698-8

M3 - Article

AN - SCOPUS:84874253959

VL - 150

SP - 671

EP - 677

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 4

ER -