A Mermin-Wagner Theorem for Gibbs States on Lorentzian Triangulations

Autor(es)

Kelbert, M. ^{[1, 2]} ; Suhov, Yu ^{[1, 3, 4]} ; Yambartsev, A. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Math & Stat, Dept Stat, Sao Paulo - Brazil

^[2] Swansea Univ, Dept Math, Swansea, W Glam - Wales

^[3] Univ Cambridge, Stat Lab, DPMMS, Cambridge - England

^[4] Russian AS, IITP, Moscow - Russia

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 150, n. 4, p. 671-677, FEB 2013.
• Citações Web of Science: 2

Resumo

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'a parts per thousand currency signd. 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. (AU)

• Processo FAPESP: 12/04372-7 - Aspectos probabilísticos em triangulações causais dinâmicas
• Beneficiário: Anatoli Iambartsev
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 11/20133-0 - Ausência de quebra de simetria contínua em sistemas quânticos bidimensionais
• Beneficiário: Anatoli Iambartsev
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional