F. Colomo, A. G. Pronko, “An approach for calculating correlation functions in the six-vertex model with domain wall boundary conditions”, TMF, 171:2 (2012), 254–270; Theoret. and Math. Phys., 171:2 (2012), 641

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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 171, Number 2, Pages 254–270
DOI: https://doi.org/10.4213/tmf8368 (Mi tmf8368)

This article is cited in 16 scientific papers (total in 16 papers)

An approach for calculating correlation functions in the six-vertex model with domain wall boundary conditions

F. Colomo^a, A. G. Pronko^b

^a INFN, Sezione di Firenze, Firenze, Italy
^b St. Petersburg Department of the Steklov Institute of Mathematics, RAS, St. Petersburg, Russia

Full-text PDF (502 kB) Citations (16)

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DOI: https://doi.org/10.4213/tmf8368

Abstract: We address the problem of calculating correlation functions in the six-vertex model with domain wall boundary conditions by considering a particular nonlocal correlation function, called the row configuration probability. This correlation function can be used as a building block for computing various (both local and nonlocal) correlation functions in the model. We calculate the row configuration probability using the quantum inverse scattering method, giving the final result in terms of multiple integrals. We also discuss the relation to the emptiness formation probability, another nonlocal correlation function, which was previously computed using similar methods.

Keywords: vertex model, correlation function, domain wall boundary condition, multiple-integral representation, quantum inverse scattering method.

Received: 17.05.2012

English version:
Theoretical and Mathematical Physics, 2012, Volume 171, Issue 2, Pages 641–654
DOI: https://doi.org/10.1007/s11232-012-0061-2

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: F. Colomo, A. G. Pronko, “An approach for calculating correlation functions in the six-vertex model with domain wall boundary conditions”, TMF, 171:2 (2012), 254–270; Theoret. and Math. Phys., 171:2 (2012), 641–654

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https://doi.org/10.4213/tmf8368

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This publication is cited in the following 16 articles:

Filippo Colomo, Andrei G. Pronko, “Scaling limit of domino tilings on a pentagonal domain”, Phys. Rev. E, 110:5 (2024)
Zhao Zhang, Henrik Schou Røising, “The frustration-free fully packed loop model”, J. Phys. A: Math. Theor., 56:19 (2023), 194001
Zhao Zhang, Israel Klich, “Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models”, SciPost Phys., 15:2 (2023)
Belov P., Reshetikhin N., “The Two-Point Correlation Function in the Six-Vertex Model”, J. Phys. A-Math. Theor., 55:15 (2022), 155001
V. S. Kapitonov, A. G. Pronko, “Six-Vertex Model as a Grassmann Integral, One-Point Function, and the Arctic Ellipse”, J Math Sci, 264:3 (2022), 313
Jean-Marie Stéphan, “Exact time evolution formulae in the XXZ spin chain with domain wall initial state”, J. Phys. A: Math. Theor., 55:20 (2022), 204003
Mikhail D. Minin, Andrei G. Pronko, “Boundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties”, SIGMA, 17 (2021), 111, 29 pp.
Colomo F., Di Giulio G., Pronko A.G., “Six-Vertex Model on a Finite Lattice: Integral Representations For Nonlocal Correlation Functions”, Nucl. Phys. B, 972 (2021), 115535
A.A. Nazarov, S. A. Paston, “Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain”, Theoret. and Math. Phys., 205:2 (2020), 1473–1491
V. S. Kapitonov, A. G. Pronko, “Six-vertex model as a Grassmann integral, one-point function, and the arctic ellipse”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 27, Zap. nauchn. sem. POMI, 494, POMI, SPb., 2020, 168–218
Cantini L., Colomo F., Pronko A.G., “Integral Formulas and Antisymmetrization Relations For the Six-Vertex Model”, Ann. Henri Poincare, 21:3 (2020), 865–884
J. Math. Sci. (N. Y.), 242:5 (2019), 742–752
Colomo F., Pronko A.G., Sportiello A., “Generalized emptiness formation probability in the six-vertex model”, J. Phys. A-Math. Theor., 49:41 (2016), 415203
Behrend R.E., “Multiply-Refined Enumeration of Alternating Sign Matrices”, Adv. Math., 245 (2013), 439–499
Falco P., “Arrow-Arrow Correlations for the Six-Vertex Model”, Phys. Rev. E, 88:3 (2013), 030103
Foda O., Wheeler M., “Partial domain wall partition functions”, J. High Energy Phys., 2012, no. 7, 186, 35 pp.

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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