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The Ising Model on the Random Planar Causal Triangulation: Bounds on the Critical Line and Magnetization Properties

Napolitano, George LU and Turova, Tatyana LU (2015) In Journal of Statistical Physics
Abstract
We investigate a Gibbs (annealed) probability measure defined on Ising spin configurations on causal triangulations of the plane. We study the region where such measure can be defined and provide bounds on the boundary of this region (critical line). We prove that for any finite random triangulation the magnetization of the central spin is sensitive to the boundary conditions. Furthermore, we show that in the infinite volume limit, the magnetization of the central spin vanishes for values of the temperature high enough.
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organization
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Contribution to journal
publication status
published
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in
Journal of Statistical Physics
publisher
Springer
external identifiers
  • scopus:84955448710
  • wos:000371086600010
ISSN
1572-9613
DOI
10.1007/s10955-015-1430-7
language
English
LU publication?
yes
id
d8cd13da-1402-4c71-8e33-7694c3027e87 (old id 8512174)
date added to LUP
2016-01-13 13:25:36
date last changed
2017-10-22 03:31:39
@article{d8cd13da-1402-4c71-8e33-7694c3027e87,
  abstract     = {We investigate a Gibbs (annealed) probability measure defined on Ising spin configurations on causal triangulations of the plane. We study the region where such measure can be defined and provide bounds on the boundary of this region (critical line). We prove that for any finite random triangulation the magnetization of the central spin is sensitive to the boundary conditions. Furthermore, we show that in the infinite volume limit, the magnetization of the central spin vanishes for values of the temperature high enough.},
  author       = {Napolitano, George and Turova, Tatyana},
  issn         = {1572-9613},
  language     = {eng},
  publisher    = {Springer},
  series       = {Journal of Statistical Physics},
  title        = {The Ising Model on the Random Planar Causal Triangulation: Bounds on the Critical Line and Magnetization Properties},
  url          = {http://dx.doi.org/10.1007/s10955-015-1430-7},
  year         = {2015},
}