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

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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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Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics
Original languageEnglish
JournalJournal of Statistical Physics
Publication statusPublished - 2015
Publication categoryResearch
Peer-reviewedYes

Bibliographic note

The article was published First Online: 21 December 2015