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

Author(s)

Hernandez, J. C. ^[1] ; Suhov, Y. ^{[1, 2, 3]} ; Yambartsev, A. ^[1] ; Zohren, S. ^{[1, 4, 5, 6]}

Affiliation

^[1] Univ Sao Paulo, Inst Math & Stat, Dept Stat, BR-05508090 Sao Paulo - Brazil

^[2] Univ Cambridge, DPMMS, Cambridge CB3 0WB - England

^[3] IITP RAS, Moscow 127994 - Russia

^[4] Univ Oxford, Rudolf Peierls Ctr Theoret Phys, Oxford OX1 3NP - England

^[5] PUC Rio de Janeiro, Dept Phys, Rio De Janeiro - Brazil

^[6] Univ Oxford, Mansfield Coll, Oxford OX1 3NP - England

• Document type: Journal article
• Source: Journal of Mathematical Physics; v. 54, n. 6 JUN 2013.
• Web of Science Citations: 4

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. (C) 2013 AIP Publishing LLC. (AU)

• FAPESP's process: 12/04372-7 - Probabilistic aspects of causal dynamical triangulations
• Grantee: Anatoli Iambartsev
• Support Opportunities: Regular Research Grants