Form Factor Representation of the Correlation Functions of the two Dimensional Ising Model on a Cylinder

Bugrij, A. I.

doi:10.1007/978-94-010-0670-5_5

Cited by 20 publications

(38 citation statements)

References 17 publications

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“…For the Ising model this was achieved in Ref. [10]. The two-point correlation functions of σ's and µ's were obtained rigorously in the form of series.…”

Section: A Possible Approachesmentioning

confidence: 99%

“…For the case of the Ising model, we show below that Eq. (6) also follows directly from the form factor approach using the results of Bugrij [10].…”

Section: A Possible Approachesmentioning

confidence: 99%

“…To understand how this is to be done in general, we employ the series expansions from Ref. [10] which will provide the necessary clues to understanding the singularity structure in this case.…”

Section: A Possible Approachesmentioning

confidence: 99%

“…Using expressions obtained in Ref. [10] from a lattice analysis of this model, we analyze the asymptotics of the spin-spin correlation functions. In doing so we are able to cast the spin-spin correlation function in a form nearly identical to what would be found using the Lehmann expansion.…”

Section: Introductionmentioning

confidence: 99%

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Low temperature correlation functions in integrable models: Derivation of the large distance and time asymptotics from the form factor expansion

Altshuler¹,

Konik²,

Tsvelik³

2006

Nuclear Physics B

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We propose an approach to the problem of low but finite temperature dynamical correlation functions in integrable one-dimensional models with a spectral gap. The approach is based on the analysis of the leading singularities of the operator matrix elements and is not model specific.We discuss only models with well defined asymptotic states. For such models the long time, large distance asymptotics of the correlation functions fall into two universality classes. These classes differ primarily by whether the behavior of the two-particle S matrix at low momenta is diagonal or corresponds to pure reflection. We discuss similarities and differences between our results and results obtained by the semi-classical method suggested by Sachdev and Young, Phys. Rev. Lett. 78, 2220Lett. 78, (1997.

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“…For the Ising model this was achieved in Ref. [10]. The two-point correlation functions of σ's and µ's were obtained rigorously in the form of series.…”

Section: A Possible Approachesmentioning

confidence: 99%

“…For the case of the Ising model, we show below that Eq. (6) also follows directly from the form factor approach using the results of Bugrij [10].…”

Section: A Possible Approachesmentioning

confidence: 99%

Section: A Possible Approachesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Low temperature correlation functions in integrable models: Derivation of the large distance and time asymptotics from the form factor expansion

Altshuler¹,

Konik²,

Tsvelik³

2006

Nuclear Physics B

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show abstract

“…Some of the most important characteristics of 2DIM include lattice correlation functions and form factors 18,19,20 . These quantities attract considerable interest in connection with the condensed-matter problems 15 , as well as with the problems in string theory 21 .…”

Section: Introductionmentioning

confidence: 99%

Characteristics of two-dimensional lattice models from a fermionic realization: Ising andXYZmodels

Khachatryan

Sedrakyan

2009

Phys. Rev. B

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We develop a field theoretical approach to the classical two-dimensional models, particularly to 2D Ising model (2DIM) and XY Z model, which is simple to apply for calculation of various correlation functions. We calculate the partition function of 2DIM and XY model within the developed framework. Determinant representation of spin-spin correlation functions is derived using fermionic realization for the Boltzmann weights. The approach also allows formulation of the partition function of 2DIM in the presence of an external magnetic field.

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Multicriticality in Yang-Lee edge singularity

Lencsés

Miscioscia

Mussardo

et al. 2023

J. High Energ. Phys.

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In this paper we study the non-unitary deformations of the two-dimensional Tricritical Ising Model obtained by coupling its two spin ℤ2 odd operators to imaginary magnetic fields. Varying the strengths of these imaginary magnetic fields and adjusting correspondingly the coupling constants of the two spin ℤ2 even fields, we establish the presence of two universality classes of infrared fixed points on the critical surface. The first class corresponds to the familiar Yang-Lee edge singularity, while the second class to its tricritical version. We argue that these two universality classes are controlled by the conformal non-unitary minimal models $$ \mathcal{M} $$ M (2, 5) and $$ \mathcal{M} $$ M (2, 7) respectively, which is supported by considerations based on PT symmetry and the corresponding extension of Zamolodchikov’s c-theorem, and also verified numerically using the truncated conformal space approach. Our results are in agreement with a previous numerical study of the lattice version of the Tricritical Ising Model [1]. We also conjecture the classes of universality corresponding to higher non-unitary multicritical points obtained by perturbing the conformal unitary models with imaginary coupling magnetic fields.

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Form Factor Representation of the Correlation Functions of the two Dimensional Ising Model on a Cylinder

Cited by 20 publications

References 17 publications

Low temperature correlation functions in integrable models: Derivation of the large distance and time asymptotics from the form factor expansion

Low temperature correlation functions in integrable models: Derivation of the large distance and time asymptotics from the form factor expansion

Characteristics of two-dimensional lattice models from a fermionic realization: Ising andXYZmodels

Multicriticality in Yang-Lee edge singularity

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