A. I. Bugrij, O. O. Lisovyy, “Correlation Function of the Two-Dimensional Ising Model on a Finite Lattice: II”, TMF, 140:1 (2004), 113–127; Theoret. and Math. Phys., 140:1 (2004), 987

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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 140, Number 1, Pages 113–127
DOI: https://doi.org/10.4213/tmf75 (Mi tmf75)

This article is cited in 26 scientific papers (total in 26 papers)

Correlation Function of the Two-Dimensional Ising Model on a Finite Lattice: II

A. I. Bugrij, O. O. Lisovyy

N. N. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine

Full-text PDF (262 kB) Citations (26)

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DOI: https://doi.org/10.4213/tmf75

Abstract: We calculate the pair correlation function and the magnetic susceptibility in the anisotropic Ising model on the lattice with one infinite and one finite dimension with periodic boundary conditions imposed along the second dimension. Using the exact expressions for lattice form factors, we propose formulas for arbitrary spin matrix elements, thus providing a possibility to calculate all multipoint correlation functions in the anisotropic Ising model on cylindrical and toroidal lattices. We analyze passing to the scaling limit.

Keywords: Ising model, correlation function, susceptibility, form factor, finite-size lattice.

Received: 28.07.2003

English version:
Theoretical and Mathematical Physics, 2004, Volume 140, Issue 1, Pages 987–1000
DOI: https://doi.org/10.1023/B:TAMP.0000033035.90327.1f

Bibliographic databases:

Language: Russian

Citation: A. I. Bugrij, O. O. Lisovyy, “Correlation Function of the Two-Dimensional Ising Model on a Finite Lattice: II”, TMF, 140:1 (2004), 113–127; Theoret. and Math. Phys., 140:1 (2004), 987–1000

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf75

https://doi.org/10.4213/tmf75

https://www.mathnet.ru/eng/tmf/v140/i1/p113

Cycle of papers

Correlation Function of the Two-Dimensional Ising Model on a Finite Lattice: I.
A. I. Bugrij
TMF, 2001, 127:1, 143–167
Correlation Function of the Two-Dimensional Ising Model on a Finite Lattice: II
A. I. Bugrij, O. O. Lisovyy
TMF, 2004, 140:1, 113–127

This publication is cited in the following 26 articles:

Gamayun O., Iorgov N., Zhuravlev Yu., “Effective Free-Fermionic Form Factors and the Xy Spin Chain”, SciPost Phys., 10:3 (2021), 070
Forrester P.J., Perk H.H., Trinh A.K., Witte N.S., “Leading Corrections to the Scaling Function on the Diagonal For the Two-Dimensional Ising Model”, J. Stat. Mech.-Theory Exp., 2019, 023106
Mei T., “Exact Expressions of Spin-Spin Correlation Functions of the Two-Dimensional Rectangular Ising Model on a Finite Lattice”, Entropy, 20:4 (2018), 277
Grosjean N., Maillet J.-M., Niccoli G., “On the Form Factors of Local Operators in the Bazhanov-Stroganov and Chiral Potts Models”, Ann. Henri Poincare, 16:5 (2015), 1103–1153
Chen Y., Doyon B., “Form Factors in Equilibrium and Non-Equilibrium Mixed States of the Ising Model”, J. Stat. Mech.-Theory Exp., 2014, P09021
Tracy C.A. Widom H., “On the Diagonal Susceptibility of the Two-Dimensional Ising Model”, J. Math. Phys., 54:12 (2013), 123302
Gavrylenko P., Iorgov N., Lisovyy O., “Form factors of twist fields in the lattice Dirac theory”, J. Phys. A: Math. Theor., 45:2 (2012), 025402
Witte N.S. Forrester P.J., “Fredholm Determinant Evaluations of the Ising Model Diagonal Correlations and their Lambda Generalization”, Stud. Appl. Math., 128:2 (2012), 183–223
Grosjean N., Niccoli G., “The Tau(2)-Model and the Chiral Potts Model Revisited: Completeness of Bethe Equations From Sklyanin's Sov Method”, J. Stat. Mech.-Theory Exp., 2012, P11005
Schuricht D. Essler F.H.L., “Dynamics in the Ising Field Theory After a Quantum Quench”, J. Stat. Mech.-Theory Exp., 2012, P04017
Iorgov N., “Form factors of the finite quantum XY-chain”, J. Phys. A: Math. Theor., 44:33 (2011), 335005
Iorgov N., Lisovyy O., “Finite-lattice form factors in free-fermion models”, J Stat Mech Theory Exp, 2011, P04011
Iorgov N., Lisovyy O., “Ising Correlations and Elliptic Determinants”, J Stat Phys, 143:1 (2011), 33–59
Huang Yu.-K., “Biorthonormal transfer-matrix renormalization-group method for non-Hermitian matrices”, Phys Rev E, 83:3, Part 1 (2011), 036702
Hystad G., “Periodic Ising Correlations”, J Math Phys, 52:1 (2011), 013302
N Iorgov, V Shadura, Yu Tykhyy, “Spin operator matrix elements in the quantum Ising chain: fermion approach”, J. Stat. Mech., 2011:02 (2011), P02028
Palmer J., Hystad G., “Spin matrix for the scaled periodic Ising model”, J Math Phys, 51:12 (2010), 123301
Iorgov N., Pakuliak S., Shadura V., Tykhyy Y., von Gehlen G., “Spin Operator Matrix Elements in the Superintegrable Chiral Potts Quantum Chain”, J Stat Phys, 139:5 (2010), 743–768
Khachatryan, S, “Characteristics of two-dimensional lattice models from a fermionic realization: Ising and XYZ models”, Physical Review B, 80:12 (2009), 125128
von Gehlen G., Iorgov N., Pakuliak S., Shadura V., “Factorized Finite-Size Ising Model Spin Matrix Elements From Separation of Variables”, J. Phys. A-Math. Theor., 42:30 (2009), 304026

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

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