Abstract
We investigate the six-vertex model on a square lattice rotated through an arbitrary angle with respect to the coordinate axes, a model recently introduced by Litvin and Priezzhev. Auxiliary vertices are used to define an inhomogeneous system which leads to a one-parameter family of commuting transfer matrices. A product of commuting transfer matrices can be interpreted as a transfer matrix acting on zigzag walls in the rotated system. Using an equation for commuting transfer matrices, we calculate their eigenvalues. Finite-size properties of the model are discussed from the viewpoint of the conformal field theory.
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References
A. A. Litvin and V. B. Priezzhev,J. Stat. Phys. 60:307–321 (1990).
H. Bethe,Z. Phys. 71:205–226 (1931).
E. H. Lieb,Phys. Rev. Lett. 18:692–694 (1967);Phys. Rev. 162:162–172 (1967).
R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).
A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov,J. Stat. phys. 34:763–774 (1984);Nucl. Phys. B 241:333–380 (1984).
J. L. Cardy, InPhase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, 1987).
C. Itzykson and J. M. Drouffe,Statistical Field Theory (Cambridge University Press, Cambridge, 1989), Chapter 9.
H. W. Blöte, J. L. Cardy, and M. P. Nightingale,Phys. Rev. Lett. 56:742–745 (1986).
H. J. de Vega and M. Karowski,Nucl. Phys. B 285:619–638 (1987).
A. Klümper and M. T. Batchelor,J. Phys. A: Math. Gen. 23:L189-L195 (1990).
A. Klümper, M. T. Batchelor, P. a. Pearce,J. Phys. A. Math. Gen. 24:3111–3133 (1991).
A. L. Owczarek and R. J. Baxter,J. Phys. A: Math. Gen. 22:1141–1165 (1989).
M. Fujimoto,J. Phys. A: Math. Gen. 27:5101–5119 (1994).
M. Wadati and Y. Akutsu,Prog. Theor. Phys. Suppl. 94:1–41 (1988).
M. Wadati, T. Deguchi, and Y. Akutsu,Phys. Rep. 180:247–332 (1989).
M. Karowski,Nucl. Phys. B 300[FS22]:473–499 (1988).
C. J. Harmer,J. Phys. A: Math. Gen. 18:L1133-L1137 (1985);J. Phys. A: Math. Gen. 19:3335–3351 (1986).
F. C. Alcaraz, M. N. Barber, and M. T. Batchelor,Ann. Phys. 182:280–343 (1988).
F. Woynarovich,Phys. Rev. Lett. 59:259–261 (1987).
A. Klümper, T. Wehner, and J. Zittartz,J Phys. A: Math. gen. 26:2815–2827 (1993).
P. A. Pearce and A. Klüper,Phys. Rev. Lett. 66:974–977 (1991).
A. Klümper and P. A. Pearce,J. Stat. Phys. 64:13–76 (1991).
M. Fujimoto,J. Stat. Phys. 67:123–154 (1992).
L. Lewin,Dilogarithms and Associated Functions (McDonald, London, 1958).
M. P. Nightingale and H. W. Blöte,J Phys. A: Math. Gen. 16:L657-L664 (1983).
J. L. Cardy,Nucl. Phys. B 270:186–204 (1986).
D. Klim and P. A. Pearce,J. Phys. A: Math. Gen. 20:L451-L456 (1987).
B. Sutherland,J. Math. Phys. 11:3183–3186 (1970).
H. N. V. Temperly and E. H. Lieb,Proc. R. Soc. Lond. A 322:251–280 (1971).
H. E. Lieb and F. Y. Wu, InPhase Transitions and Critical Phenomena, Vol. 1, C. Domb and M. S. Green, eds. (Academic Press, London, 1972).
J. Suzuki, Y. Akutsu, and M. Wadati,J. Phys. Soc. Jpn. 59:2667–2680 (1990).
I. Affleck,Phys. Rev. Lett. 56:746–748 (1986).
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Fujimoto, M. Six-vertex model with rotated boundary conditions. J Stat Phys 82, 1519–1539 (1996). https://doi.org/10.1007/BF02183394
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DOI: https://doi.org/10.1007/BF02183394