Abstract
At the critical temperature in the 2d Ising model on the square lattice, we establish the rotational invariance of the spin-spin correlation function using the asymptotics of the spin-spin correlation function along special directions (McCoy and Wu in the two dimensional Ising model. Harvard University Press, Cambridge, 1973) and the finite difference Hirota equation for which the spin-spin correlation function is shown to satisfy (Perk in Phys Lett A 79:3–5, 1980; Perk in Proceedings of III international symposium on selected topics in statistical mechanics, Dubna, August 22–26, 1984, JINR, vol II, pp 138–151, 1985).
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Montroll E., Potts R., Ward J.: Correlations and Spontaneous Magnetization of the Two-Dimensional Ising Model. J. Math. Phys. 4, 308–322 (1963)
McCoy, B., Wu, T.: The Two Dimensional Ising Model. Cambridge, MA: Harvard University Press, 1973
Perk J.H.H.: Quadratic identities for Ising model correlations. Phys. Lett. 79A, 3–5 (1980)
Perk, J.H.H., Au-Yang, H.: Ising models and soliton equations. In: Proc. III International Symposium on Selected Topics in Statistical Mechanics (Dubna, August 22–26, 1984), Dubna, USSR: JINR, 1985, Vol. II, pp. 138–151
Sato, M., Miwa, T., Jimbo, M.: Studies on Holonomic Quantum Fields. I-V, Proc. Japan Acad. A 53, 6–10, 147–152, 153–158, 183–185, 219–224 (1977)
Schrader, R.: New correlation inequalities for the Ising and P(phi) theories. Phy. Rev. B (Solid State) 15, issue 5, March 1, 2798–2803 (1977)
Serrin J.: On the Harnack inequality for linear elliptic equations. J. d’Anal. Math. 4(1), 292–308 (1955)
Wu T., McCoy B., Tracy C., Barouch E.: Spin-spin Correlation Functions for the Two-Dimensional Ising Model: Exact Theory in the Scaling Region. Phys. Rev. B. 13, 316–374 (1976)
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Communicated by S. Smirnov
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Pinson, H. Rotational Invariance of the 2d Spin – Spin Correlation Function. Commun. Math. Phys. 314, 807–816 (2012). https://doi.org/10.1007/s00220-012-1545-5
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DOI: https://doi.org/10.1007/s00220-012-1545-5