A Mermin-Wagner Theorem for Gibbs States on Lorentzian Triangulations

M. Kelbert, Yu Suhov, A. Yambartsev

Research output: Contribution to journalArticle

2 Citations (Scopus)

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′≤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.

Original languageEnglish (US)
Pages (from-to)671-677
Number of pages7
JournalJournal of Statistical Physics
Volume150
Issue number4
DOIs
StatePublished - Feb 11 2013

Fingerprint

Gibbs States
triangulation
Triangulation
Gibbs Measure
theorems
Torus
Theorem
Galton-Watson Tree
Invariant Mean
Quantum Gravity
Group Action
Symmetry Breaking
triangles
Triangle
Nearest Neighbor
broken symmetry
apexes
gravitation
Invariant
Model

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Kelbert, M. ; Suhov, Yu ; Yambartsev, A. / A Mermin-Wagner Theorem for Gibbs States on Lorentzian Triangulations. In: Journal of Statistical Physics. 2013 ; Vol. 150, No. 4. pp. 671-677.
@article{2a0438462081400da62b579fed71f906,
title = "A Mermin-Wagner Theorem for Gibbs States on Lorentzian Triangulations",
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′≤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.",
author = "M. Kelbert and Yu Suhov and A. Yambartsev",
year = "2013",
month = "2",
day = "11",
doi = "10.1007/s10955-013-0698-8",
language = "English (US)",
volume = "150",
pages = "671--677",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "4",

}

A Mermin-Wagner Theorem for Gibbs States on Lorentzian Triangulations. / Kelbert, M.; Suhov, Yu; Yambartsev, A.

In: Journal of Statistical Physics, Vol. 150, No. 4, 11.02.2013, p. 671-677.

Research output: Contribution to journalArticle

TY - JOUR

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

AU - Kelbert, M.

AU - Suhov, Yu

AU - Yambartsev, A.

PY - 2013/2/11

Y1 - 2013/2/11

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.

UR - http://www.scopus.com/inward/record.url?scp=84874253959&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874253959&partnerID=8YFLogxK

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 -