Bounds on the critical line via transfer matrix methods for an Ising model coupled to causal dynamical triangulations

J. C. Hernandez, Y. Suhov, A. Yambartsev, S. Zohren

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Abstract

We introduce a transfer matrix formalism for the (annealed) Ising model coupled to two-dimensional causal dynamical triangulations. Using the Krein-Rutman theory of positivity preserving operators we study several properties of the emerging transfer matrix. In particular, we determine regions in the quadrant of parameters β, μ > 0 where the infinite-volume free energy converges, yielding results on the convergence and asymptotic properties of the partition function and the Gibbs measure.

Original languageEnglish (US)
Article number063301
JournalJournal of Mathematical Physics
Volume54
Issue number6
DOIs
Publication statusPublished - Jun 3 2013

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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