×

Form factors in the Bullough-Dodd-related models: the Ising model in a magnetic field. (English. Russian original) Zbl 1284.82013

Theor. Math. Phys. 173, No. 2, 1518-1540 (2012); translation from Teor. Mat. Fiz. 173, No. 2, 219-244 (2012).
Summary: We consider a certain modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particle minimal form factors are eliminated from the construction. We consequently obtain a convenient representation for the multiparticle form factors, establish recurrence relations between them, and study their properties. We use the proposed construction to obtain the free-field representation of form factors for the lightest particles in the \(\Phi_{1,2}\)-perturbed minimal models. As an important example, we consider the Ising model in a magnetic field. We verify that the results obtained in the framework of the proposed free-field representation agree with the corresponding results obtained by solving the bootstrap equations.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82D40 Statistical mechanics of magnetic materials
81T25 Quantum field theory on lattices
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B, 241, 333–380 (1984). · Zbl 0661.17013 · doi:10.1016/0550-3213(84)90052-X
[2] A. B. Zamolodchikov, ”Integrable field theory from conformal field theory,” in: Integrable Systems in Quantum Field Theory and Statistical Mechanics (Adv. Studies Pure Math., Vol. 19, M. Jimbo, T. Miwam, and A. Tsuchiya, eds.), Acad. Press, Boston, Mass. (1989), pp. 641–674.
[3] A. B. Zamolodchikov, Internat. J. Mod. Phys. A, 4, 4235–4248 (1989). · doi:10.1142/S0217751X8900176X
[4] G. Takács, Nucl. Phys. B, 489, 532–556 (1997); arXiv:hep-th/9604098v5 (1996). · Zbl 0925.81054 · doi:10.1016/S0550-3213(97)00057-6
[5] N. Reshetikhin and F. Smirnov, Commun. Math. Phys., 131, 157–177 (1990). · Zbl 0723.35077 · doi:10.1007/BF02097683
[6] D. Bernard and A. LeClair, Nucl. Phys. B, 340, 721–751 (1990). · doi:10.1016/0550-3213(90)90466-Q
[7] F. A. Smirnov, Internat. J. Mod. Phys. A, 6, 1407–1428 (1991). · doi:10.1142/S0217751X91000745
[8] C. J. Efthimiou, Nucl. Phys. B, 398, 697–740 (1993). · doi:10.1016/0550-3213(93)90609-S
[9] F. A. Smirnov, Form Factors in Completely Integrable Models of Quantum Field Theories (Adv. Ser. Math. Phys., Vol. 14), World Scientific, Singapore (1992). · Zbl 0788.46077
[10] J. Cardy and G. Mussardo, Nucl. Phys. B, 340, 387–402 (1990). · doi:10.1016/0550-3213(90)90452-J
[11] G. Delfino, G. Mussardo, and P. Simonetti, Nucl. Phys. B, 473, 469–508 (1996); arXiv:hep-th/9603011v1 (1996). · Zbl 0925.81296 · doi:10.1016/0550-3213(96)00265-9
[12] A. Zamolodchikov and I. Ziyatdinov, Nucl. Phys. B, 849, 654–674 (2011). · Zbl 1215.82027 · doi:10.1016/j.nuclphysb.2011.04.005
[13] G. Delfino, P. Grinza, and G. Mussardo, Nucl. Phys. B, 737, 291–303 (2006). · Zbl 1109.82310 · doi:10.1016/j.nuclphysb.2005.12.024
[14] B. Pozsgay and G. Takács, Nucl. Phys. B, 788, 167–208 (2008). · Zbl 1220.81161 · doi:10.1016/j.nuclphysb.2007.06.027
[15] B. Pozsgay and G. Takács, Nucl. Phys. B, 788, 209–251 (2008); arXiv:0706.3605v1 [hep-th] (2007). · Zbl 1220.81162 · doi:10.1016/j.nuclphysb.2007.07.008
[16] A. Koubek and G. Mussardo, Phys. Lett. B, 311, 193–201 (1993); arXiv:hep-th/9306044v1 (1993). · doi:10.1016/0370-2693(93)90554-U
[17] A. Fring, G. Mussardo, and P. Simonetti, Nucl. Phys. B, 393, 413–441 (1993); arXiv:hep-th/9211053v1 (1992). · Zbl 1245.81238 · doi:10.1016/0550-3213(93)90252-K
[18] R. K. Dodd and R. K. Bullough, Proc. Roy. Soc. London A, 352, 481–503 (1977). · doi:10.1098/rspa.1977.0012
[19] A. Fring, A. Mussardo, and P. Simonetti, Phys. Lett. B, 307, 83–90 (1993). · doi:10.1016/0370-2693(93)90196-O
[20] C. Acerbi, Nucl. Phys. B, 497, 589–610 (1997); arXiv:hep-th/9701062v1 (1997). · Zbl 0934.81054 · doi:10.1016/S0550-3213(97)00303-9
[21] S. L. Lukyanov, Commun. Math. Phys., 167, 183–226 (1995); arXiv:hep-th/9307196v1 (1993). · Zbl 0818.46079 · doi:10.1007/BF02099357
[22] S. L. Lukyanov, Modern Phys. Lett. A, 12, 2543–2250 (1997); arXiv:hep-th/9703190v2 (1997). · Zbl 0902.35099 · doi:10.1142/S0217732397002673
[23] S. L. Lukyanov, Phys. Lett. B, 408, 192–200 (1997); arXiv:hep-th/9704213v1 (1997). · Zbl 0905.17028 · doi:10.1016/S0370-2693(97)00767-3
[24] V. A. Fateev and M. Lashkevich, Nucl. Phys. B, 696, 301–350 (2004); arXiv:hep-th/0402082v2 (2004). · Zbl 1236.81132 · doi:10.1016/j.nuclphysb.2004.06.043
[25] V. A. Fateev, V. V. Postnikov, and Y. P. Pugai, JETP Lett., 83, 172–178 (2006); arXiv:hep-th/0601073v1 (2006). · doi:10.1134/S0021364006040096
[26] V. A. Fateev and Y. P. Pugai, J. Phys. A, 42, 304013 (2009). · Zbl 1179.82028 · doi:10.1088/1751-8113/42/30/304013
[27] Y. Hara, M. Jimbo, H. Konno, S. Odake, and J. Shiraishi, ”Free field approach to the dilute A L models,” arXiv:math/9902150v1 (1999). · Zbl 0969.81024
[28] V. A. Brazhnikov and S. L. Lukyanov, Nucl. Phys. B, 512, 616–636 (1998); arXiv:hep-th/9707091v1 (1997). · doi:10.1016/S0550-3213(97)00713-X
[29] B. Feigin and M. Lashkevich, J. Phys. A, 42, 304014 (2009). · Zbl 1177.81121 · doi:10.1088/1751-8113/42/30/304014
[30] O. Alekseev and M. Lashkevich, JHEP, 1007, 095 (2010); arXiv:0912.5225v4 [hep-th] (2009). · Zbl 1290.81051 · doi:10.1007/JHEP07(2010)095
[31] V. Fateev, S. Lukyanov, A. Zamolodchikov, and Al. Zamolodchikov, Nucl. Phys. B, 516, 652–674 (1998); arXiv:hep-th/9709034v1 (1997). · Zbl 0909.58074 · doi:10.1016/S0550-3213(98)00002-9
[32] A. Koubek, Internat. J. Mod. Phys. A, 9, 1909–1927 (1994); arXiv:hep-th/9211134v1 (1992). · Zbl 0985.81704 · doi:10.1142/S0217751X94000820
[33] G. Delfino and G. Mussardo, Nucl. Phys. B, 455, 724–758 (1995). · Zbl 0925.82042 · doi:10.1016/0550-3213(95)00464-4
[34] G. Delfino, P. Simonetti, and J. L. Cardy, Phys. Lett. B, 387, 327–333 (1996); arXiv:hep-th/9607046v1 (1996). · doi:10.1016/0370-2693(96)01035-0
[35] G. Mussardo and P. Simonetti, Internat. J. Mod. Phys. A, 9, 3307–3337 (1994); arXiv:hep-th/9308057v1 (1993). · Zbl 0985.81712 · doi:10.1142/S0217751X94001308
[36] V. A. Fateev, Phys. Lett. B, 324, 45–51 (1994). · doi:10.1016/0370-2693(94)00078-6
[37] R. Guida and N. Magnoli, Phys. Lett. B, 411, 127–133 (1997); arXiv:hep-th/9706017v2 · doi:10.1016/S0370-2693(97)00983-0
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.