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Marginal Densities, Factor Graph Duality, and High-Temperature Series Expansions [article]

Mehdi Molkaraie
2020 arXiv   pre-print
We prove that the marginal densities of a global probability mass function in a primal normal factor graph and the corresponding marginal densities in the dual normal factor graph are related via local  ...  graph of the model.  ...  ., for his comments and for his continued support. The author also wishes to thank J. Dauwels, P. Vontobel, V. Gómez, and B. Ghojogh for their comments.  ... 
arXiv:1901.02733v3 fatcat:4lpt6pzlebcarbgewhvnwcge4q

Finite temperature bosonic closed strings: Thermal duality and the Kosterlitz-Thouless transition

Shyamoli Chaudhuri
2002 Physical Review D, Particles and fields  
Invariance of the path integral under modular transformations gives a thermal duality invariant expression for the free energy of free closed strings at finite temperature.  ...  Our starting point is the intensive generating functional of connected one-loop closed vacuum string graphs given by the Polyakov path integral.  ...  Shapere, and C. Vafa for their questions. This research was supported in part by the award of grant NSF-PHY-9722394 by the National Science Foundation under the auspices of the Career program.  ... 
doi:10.1103/physrevd.65.066008 fatcat:zn57nwbf2fa2bn6uaf5smeys5y

Thermal Duality and the String Canonical Ensemble [article]

Shyamoli Chaudhuri
2005 arXiv   pre-print
We present both the low and high temperature expansions for the one-loop heterotic and type I string free energies, results which follow from an explicit term-by-term evaluation of the modular integrals  ...  , and determined uniquely by thermal duality.  ...  This research has been supported in part by the National Science Foundation, the Aspen Center for Physics, and the Kavli Institute for Theoretical Physics.  ... 
arXiv:hep-th/0506143v6 fatcat:gc6iex4xznh4hgy65v5moc6lha

Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank

Yi Jiang, Ilya Dumer, Alexey A. Kovalev, Leonid P. Pryadko
2019 Journal of Mathematical Physics  
With the help of duality and a known bound on high-order cumulants, we established the absolute convergence of both the high-and low-temperature series expansions of the free energy density in finite regions  ...  To this end, consider the high-temperature series (HTS) expansion of the free energy density (2), fe(Θ; K, h) ≡ ∞ ∑ s=1 κ (s) e (Θ; J, h ′ ) β s s!  ...  density in the circle Lemma 5.  ... 
doi:10.1063/1.5039735 fatcat:fu4tjqdpnrht3kxwtrv27s7sli

Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank [article]

Yi Jiang and Ilya Dumer and Alexey A. Kovalev and Leonid P. Pryadko
2018 arXiv   pre-print
We also discuss the convergence of the high- and low-temperature series for the free energy density, prove the analyticity of limiting f(T) at high and low temperatures, and construct inequalities for  ...  Namely, for these infinite graphs, we show that critical temperatures with free and wired boundary conditions differ, T_c^(f)<T_c^(w).  ...  With the help of duality and a known bound on highorder cumulants, we established the absolute convergence of both the high-and low-temperature series expansions of the free energy density in finite regions  ... 
arXiv:1805.00644v2 fatcat:antlo62mtjcojlig4bs7fcuuui

Thermal Duality Transformations and the Canonical Ensemble: The Deconfining Long String Phase Transition [article]

Shyamoli Chaudhuri
2005 arXiv   pre-print
We demonstrate that each exhibits a T^2 growth in the free energy at high temperatures far above the string scale.  ...  thermal dual string theories, type IB and type I'.  ...  I would like to acknowledge Joe Polchinski for urging me to be more precise in applying the thermal (Euclidean T-duality) transformations linking the thermal vacua of the six Lorentz invariant 10D supersymmetric  ... 
arXiv:hep-th/0409301v10 fatcat:5ztrd4ki7rbpxmzjqhy7wb6bne

Deformations of Lifshitz holography

Miranda C. N. Cheng, Sean A. Hartnoll, Cynthia A. Keeler
2010 Journal of High Energy Physics  
The simplest gravity duals for quantum critical theories with z=2 'Lifshitz' scale invariance admit a marginally relevant deformation.  ...  Generic black holes in the bulk describe the field theory with a dynamically generated momentum scale Lambda as well as finite temperature T.  ...  The main fact that restricts us to the high temperature regime is that the truncated counterterm series is more accurate there.  ... 
doi:10.1007/jhep03(2010)062 fatcat:hpcur72sojh7zetgwujqghalle

Heterotic type I strings at high temperature

Shyamoli Chaudhuri
2018 Physical Review D  
We show that the high temperature limits of the heterotic E8xE8 and Spin(32)/Z2 strings and their Type I A/B superstring duals are finite and convergent.  ...  the annulus graph alone.  ...  t-high temperature-behavior of the three individual open and unoriented one-loop type IB superstring graphs.  ... 
doi:10.1103/physrevd.98.046017 fatcat:i7tiklliurgsrjzdqyghomamla

Effective actions and bubble nucleation from holography [article]

Fëanor Reuben Ares, Oscar Henriksson, Mark Hindmarsh, Carlos Hoyos, Niko Jokela
2021 arXiv   pre-print
We discuss the computation of the quantum effective action of strongly interacting field theories using holographic duality, and its use to determine quasi-equilibrium parameters of first order phase transitions  ...  Despite the simplicity, the model contains a rich phase diagram, including first order phase transitions at non-zero temperature, due to various multi-trace deformations.  ...  Although our analysis is motivated by its possible application to cosmological transitions and thus limited to high temperature and zero charge density, it can be straightforwardly generalised to other  ... 
arXiv:2109.13784v2 fatcat:f4mgplba2fhipnu6chcp36bhoe

Universal amplitude ratios in the 2D four-state Potts model

Michele Caselle, Roberto Tateo, Stefano Vinti
1999 Nuclear Physics B  
Our results are compatible with those recently obtained using the form-factors approach and with the existing low temperature series for the model.  ...  We simulated the model close to criticality in both phases taking care to keep the systematic errors, due to finite size effects and logarithmic corrections in the scaling functions, under control.  ...  Acknowledgements We thank J.L.Cardy, G.Delfino, P.Dorey, F.Gliozzi and B.Nienhuis for helpful discussions. This work was partially supported by the European Commission TMR programme ERBFMRX-CT96-0045.  ... 
doi:10.1016/s0550-3213(99)00521-0 fatcat:xmwl5dksybastbfz47jivsinl4

Holography and the Canonical Ensemble of Fermionic Strings [article]

Shyamoli Chaudhuri
2005 arXiv   pre-print
: the growth of the number of degrees of freedom in the free energy at high temperatures is identical to that in a two-dimensional quantum field theory.  ...  We clarify the precise nature of the thermal duality phase transition in each case, confirming that it lies within the Kosterlitz-Thouless universality class.  ...  Also new is the observed connection between the spontaneously broken thermal duality, and the signal for a phase transition to a holographic phase at high temperatures: the growth with temperature in the  ... 
arXiv:hep-th/0407137v7 fatcat:5zkixhsubvhwnlfhfyk63iimgy

Aperiodic Ising Models [article]

Uwe Grimm, Michael Baake
1996 arXiv   pre-print
Here, duality arguments and exact solutions in the sense of commuting transfer matrices are used to gain information about the critical behaviour.  ...  We also investigate the zero-field Ising model on two-dimensional aperiodic graphs, which are constructed from rectangular grids in the same spirit as the so-called Labyrinth.  ...  We also thank Robert Grifths, Albertus Hof and Laurent Raymond for valuable discussions during the workshop.  ... 
arXiv:cond-mat/9604116v1 fatcat:zrijvbptbrgpdnbfqq7vrikjqa

Norm-Product Belief Propagation: Primal-Dual Message-Passing for Approximate Inference

Tamir Hazan, Amnon Shashua
2010 IEEE Transactions on Information Theory  
based on "convex-free-energy" and linear-programming (LP) relaxation as a zero-temperature of a convex-free-energy.  ...  In this paper, we treat both forms of probabilistic inference, estimating marginal probabilities of the joint distribution and finding the most probable assignment, through a unified message-passing algorithm  ...  Globerson, and Y. Weiss for helpful discussions. They also thank the anonymous referees for their criticisms and suggestions.  ... 
doi:10.1109/tit.2010.2079014 fatcat:a3qwgbme5jdr3iyikqvsaohcfa

High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials

Masayuki Ohzeki, Jesper Lykke Jacobsen
2015 Journal of Physics A: Mathematical and Theoretical  
Similar precision is found throughout the high-temperature part of the phase diagram.  ...  We propose a duality analysis for obtaining the critical manifold of two-dimensional spin glasses.  ...  Scullard, and Koujin Takeda.  ... 
doi:10.1088/1751-8113/48/9/095001 fatcat:bexov45jxbe7jkdpzb6z6i7n7m

Why Renormalizable NonCommutative Quantum Field Theories? [article]

Vincent Rivasseau
2007 arXiv   pre-print
We also suggest that by gluing together many Grosse-Wulkenhaar theories at high energy one can obtain an effective commutative field theory at lower energy.  ...  One of the main arguments for supersymmetry is that it makes the three flows of the standard model U (1), SU (2) and SU (3) couplings better converge at a single unification scale (see [69] and references  ...  It relies on adding to the usual propagator a marginal harmonic potential, as required by Langmann-Szabo duality [23] .  ... 
arXiv:0711.1748v1 fatcat:fbaozru32jgx3ot7kw4jb4ujfe
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