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

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

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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 language	English (US)
Article number	063301
Journal	Journal of Mathematical Physics
Volume	54
Issue number	6
DOIs	https://doi.org/10.1063/1.4808101
State	Published - Jun 3 2013

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.4808101

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@article{2f62ee2aa95844708e4603cc48ea7564,

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

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.",

author = "Hernandez, \{J. C.\} and Y. Suhov and A. Yambartsev and S. Zohren",

note = "Funding Information: This work was supported by FAPESP 2012/04372-7. J.C.H. acknowledges support by CAPES. Y.S. would like to thank the FAPESP foundation for the financial support and NUMEC, IME University of S{\~a}o Paulo, for warm hospitality. The work of A.Y. was partially supported by CNPq 308510/2010-0. The work of S.Z. was partially supported by FAPERJ 111.859/2012, CNPq 307700/2012-7, and PUC-Rio. Further, he thanks the IME at the University of S{\~a}o Paulo, as well as the Rudolf Peierls Centre for Theoretical Physics and Mansfield College, University of Oxford for kind hospitality and financial support during visits.",

year = "2013",

month = jun,

day = "3",

doi = "10.1063/1.4808101",

language = "English (US)",

volume = "54",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

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TY - JOUR

T1 - Bounds on the critical line via transfer matrix methods for an Ising model coupled to causal dynamical triangulations

AU - Hernandez, J. C.

AU - Suhov, Y.

AU - Yambartsev, A.

AU - Zohren, S.

N1 - Funding Information: This work was supported by FAPESP 2012/04372-7. J.C.H. acknowledges support by CAPES. Y.S. would like to thank the FAPESP foundation for the financial support and NUMEC, IME University of São Paulo, for warm hospitality. The work of A.Y. was partially supported by CNPq 308510/2010-0. The work of S.Z. was partially supported by FAPERJ 111.859/2012, CNPq 307700/2012-7, and PUC-Rio. Further, he thanks the IME at the University of São Paulo, as well as the Rudolf Peierls Centre for Theoretical Physics and Mansfield College, University of Oxford for kind hospitality and financial support during visits.

PY - 2013/6/3

Y1 - 2013/6/3

N2 - 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.

AB - 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.

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UR - https://www.scopus.com/pages/publications/84880124465#tab=citedBy

U2 - 10.1063/1.4808101

DO - 10.1063/1.4808101

M3 - Article

AN - SCOPUS:84880124465

SN - 0022-2488

VL - 54

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 6

M1 - 063301

ER -

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

Abstract

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