| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [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
Total Affiliations: 4
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| Document type: | Journal article |
| Source: | Journal of Statistical Physics; v. 150, n. 4, p. 671-677, FEB 2013. |
| Web of Science Citations: | 2 |
| 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 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) | |
| FAPESP's process: | 12/04372-7 - Probabilistic aspects of causal dynamical triangulations |
| Grantee: | Anatoli Iambartsev |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 11/20133-0 - Absence of continuous symmetry-breaking in 2-dimensional quantum systems |
| Grantee: | Anatoli Iambartsev |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |