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

doi:10.1063/1.4808101

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

Mathematical Physics 2013-07-15 v2 math.MP Probability

Authors: 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 beta, mu >0 where the infinite-volume free energy converges, yielding results on the convergence and asymptotic properties of the partition function and the Gibbs measure.

Keywords

Ising model causal dynamical triangulations transfer matrix Krein-Rutman theory critical line free energy Gibbs measure

Cite

@article{arxiv.1301.1483,
  title  = {Bounds on the critical line via transfer matrix methods for an Ising model coupled to causal dynamical triangulations},
  author = {J. C. Hernandez and Y. Suhov and A. Yambartsev and S. Zohren},
  journal= {arXiv preprint arXiv:1301.1483},
  year   = {2013}
}

Comments

28 pages, 4 figures, minor changes in main text, title changed, as published

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

Abstract

Keywords

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