Geodesic
A possible combinatorial point for the XYZ spin chain
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 2, pp. 179-195 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We formulate and discuss several conjectures related to the ground state vectors of odd-length XYZ spin chains with periodic boundary conditions and a special choice of the Hamiltonian parameters. In particular, we argue for the validity of a sum rule for the vector components that in a sense describes the degree of antiferromagneticity of the chain.
Keywords: XYZ spin chain, ground state, combinatorial point, sum rule. 
@article{TMF_2010_164_2_a0,
     author = {A. V. Razumov and Yu. G. Stroganov},
     title = {A~possible combinatorial point for {the~XYZ} spin chain},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {179--195},
     year = {2010},
     volume = {164},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_164_2_a0/}
}
TY  - JOUR
AU  - A. V. Razumov
AU  - Yu. G. Stroganov
TI  - A possible combinatorial point for the XYZ spin chain
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2010
SP  - 179
EP  - 195
VL  - 164
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2010_164_2_a0/
LA  - ru
ID  - TMF_2010_164_2_a0
ER  - 
%0 Journal Article
%A A. V. Razumov
%A Yu. G. Stroganov
%T A possible combinatorial point for the XYZ spin chain
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2010
%P 179-195
%V 164
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2010_164_2_a0/
%G ru
%F TMF_2010_164_2_a0
A. V. Razumov; Yu. G. Stroganov. A possible combinatorial point for the XYZ spin chain. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 2, pp. 179-195. http://geodesic.mathdoc.fr/item/TMF_2010_164_2_a0/

[1] B. Sutherland, J. Math. Phys., 11:11 (1970), 3183–3186 | DOI

[2] R. J. Baxter, Phys. Rev. Lett., 26:14 (1971), 832–833 | DOI

[3] R. J. Baxter, Ann. Phys., 70:1 (1972), 193–228 | DOI | MR | Zbl

[4] R. J. Baxter, Phys. Rev. Lett., 26:14 (1971), 834–834 | DOI

[5] R. J. Baxter, Ann. Phys., 70:2 (1972), 323–337 | DOI | MR

[6] R. J. Baxter, “Solving models in statistical mechanics”, Integrable Systems in Quantum Field Theory and Statistical Mechanics, Adv. Stud. Pure Math., 19, eds. M. Jimbo, T. Miwa, A. Tsuchiya, Math. Soc. Japan, Tokyo; Academic Press, Boston, MA, 1989, 95–116 | MR | Zbl

[7] Yu. G. Stroganov, “The 8-vertex model with a special value of the crossing parameter and the related $XYZ$ spin chain”, Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory, NATO Sci. Ser. II Math. Phys. Chem., 35, eds. S. Pakulyak, G. von Gehlen, Kluwer, Dordrecht, 2001, 315–319 | MR | Zbl

[8] X. Yang, P. Fendley, J. Phys. A, 37:38 (2004), 8937–8948, arXiv: cond-mat/0404682 | DOI | MR | Zbl

[9] G. Veneziano, J. Wosiek, JHEP, 2006:11 (2006), 030, 18 pp., arXiv: hep-th/0609210 | DOI | MR

[10] A. V. Razumov, Yu. G. Stroganov, P. Zinn-Justin, J. Phys. A, 40:39 (2007), 11827–11847, arXiv: 0704.3542 | DOI | MR | Zbl

[11] V. Fridkin, Yu. Stroganov, D. Zagier, J. Phys. A, 33:13 (2000), L121–L125, arXiv: hep-th/9912252 | DOI | MR | Zbl

[12] V. Fridkin, Yu. Stroganov, D. Zagier, J. Stat. Phys., 102:3–4 (2001), 781–794, arXiv: nlin/0010021 | DOI | MR | Zbl

[13] Yu. G. Stroganov, J. Phys. A, 34:13 (2001), L179–L185, arXiv: cond-mat/0012035 | DOI | MR | Zbl

[14] Yu. G. Stroganov, TMF, 129:2 (2001), 345–359 | DOI | MR | Zbl

[15] A. V. Razumov, Yu. G. Stroganov, J. Phys. A, 34:14 (2001), 3185–3190, arXiv: cond-mat/0012141 | DOI | MR | Zbl

[16] A. V. Razumov, Yu. G. Stroganov, J. Stat. Mech., 2006:7 (2006), P07004, 12 pp., arXiv: math-ph/0605004 | DOI | MR

[17] N. Kitanine, J. M. Maillet, N. A. Slavnov, V. Terras, J. Phys. A, 35:27 (2002), L385–L388, arXiv: hep-th/0201134 | DOI | MR | Zbl

[18] N. Kitanine, J. M. Maillet, N. A. Slavnov, V. Terras, J. Phys. A, 35:49 (2002), L753–L758, arXiv: hep-th/0210019 | DOI | MR | Zbl

[19] P. Di Francesco, P. Zinn-Justin, J.-B. Zuber, J. Stat. Mech., 2006:8 (2006), P08011, arXiv: math-ph/0603009 | DOI

[20] M. T. Batchelor, J. de Gier, B. Nienhuis, J. Phys. A, 34:19 (2001), L265–L270, arXiv: cond-mat/0101385 | DOI | MR | Zbl

[21] A. V. Razumov, Yu. G. Stroganov, J. Phys. A, 34:26 (2001), 5335–5340, arXiv: cond-mat/0102247 | DOI | MR | Zbl

[22] V. V. Bazhanov, V. V. Mangazeev, J. Phys. A, 38:8 (2005), L145–L153, arXiv: hep-th/0411094 | DOI | MR | Zbl

[23] V. V. Bazhanov, V. V. Mangazeev, J. Phys. A, 39:39 (2006), 12235–12243, arXiv: hep-th/0602122 | DOI | MR | Zbl

[24] R. Bekster, Tochno reshaemye modeli v statisticheskoi mekhanike, Mir, M., 1985 | MR | MR | Zbl

[25] Yu. G. Stroganov, Phys. Lett. A, 74:1–2 (1979), 116–118 | DOI | MR

[26] R. J. Baxter, “Exactly solved models”, Fundamental Problems in Statistical Mechanics V, ed. E. G. D. Cohen, North Holland, Amsterdam, New York, 1980, 109–141 | MR

[27] R. J. Baxter, J. Stat. Phys., 28:1 (1982), 1–41 | DOI | MR

[28] D. P. Robbins, Symmetry classes of alternating sign matrices, arXiv: math.CO/0008045

[29] G. Kuperberg, Ann. Math., 156:3 (2002), 835–866, arXiv: math.CO/0008184 | DOI | MR | Zbl

[30] A. V. Razumov, Yu. G. Stroganov, TMF, 141:3 (2004), 323–347, arXiv: math-ph/0312071 | DOI | MR | Zbl

[31] W. H. Mills, D. P. Robbins, H. Rumsey Jr., J. Combin. Theory Ser. A, 34:3 (1983), 340–359 | DOI | MR | Zbl