Abstract
We present an exact derivation for the asymptotic large distance behavior of the spin two-point correlation function in the XY-model. This allows for the exact obtainment of the critical exponent η=1/4 at the Kosterlitz--Thouless transition that occurs in this model and in the 2D neutral Coulomb gas and which has been previously obtained by scaling arguments. In order to do that, we use the language of sine-Gordon theory to obtain a Coulomb Gas description of the XY-model spin correlation function, which becomes identified with the soliton correlator of that theory. Using a representation in terms of bipolar coordinates we obtain an exact expression for the asymptotic large distance behavior of the relevant correlator at β 2=8π, which corresponds to the Kosterlitz--Thouless transition. The result is obtained by approaching this point from the plasma (high-temperature) phase of the gas. The vortex correlator of the XY-model is also obtained using the same procedure.
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References
S. Samuel (1978) Phys. Rev. D 18 1916
J.M. Kosterlitz (1994) J. Phys. C: Solid State Phys. 7 1046
A. B. Zamolodchikov and Al. B. Zamolodchikov, Ann. Phys. (NY) 120:253 (1979); V. E. Korepin, Commun. Math.
A. Luther V. J. Emery (1974) Phys. Rev. Lett. 33 589
C. Destri H. J. de Vega (1995) Nucl. Phys. B. 438 413
S. Lukyanov A. Zamolodchikov (1997) Nucl. Phys. B. 493 571
S. Lukyanov A. Zamolodchikov (2001) Nucl. Phys. B. 607 437
L. Samaj B. Jancovici (2002) J. Stat. Phys. 106 323
L. Samaj (2003) J. Phys. A: Math. Gen. 36 5913
L. Samaj I. Travenec (2000) J. Stat. Phys. 101 713
P. Kalinay L. Samaj (2002) J. Stat. Phys. 106 857
A. Alastuey F. Cornu (1992) J. Stat. Phys. 66 165
J. M. Kosterlitz D. J. Thouless (1973) J. Phys. C: Solid State Phys. 6 1181
J. V. José et al. (1977) Phys. Rev. B. 16 1217
D. J. Amit et al. (1980) J. Phys. A. Math. Gen. 13 585
T. Giamarchi H. J. Schulz (1989) Phys. Rev. B. 39 4620
P. Minnhagen (1987) Rev. Mod. Phys. 59 1001
P. J. Forrester (1996) J. Stat. Phys. 84 359
S. Mandelstam (1975) Phys. Rev. D. 11 3026
A. M. Tsvelik (1995) Quantum Field Theory in Condensed Matter Physics Cambridge University Press Cambridge
E. C. Marino J. A. Swieca (1980) Nucl. Phys. B. 170[FS1] 175
A. Lima-Santos E. C. Marino (1989) J. Stat. Phys. 55 157
S. Coleman (1975) Phys. Rev. D. 11 2088
G. Arfken (1970) Mathematical Methods for Physicists EditionNumber2 Academic Press Inc., New York
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Mondaini, L., Marino, E.C. Sine-Gordon/Coulomb Gas Soliton Correlation Functions and an Exact Evaluation of the Kosterlitz--Thouless Critical Exponent. J Stat Phys 118, 767–779 (2005). https://doi.org/10.1007/s10955-004-8828-y
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DOI: https://doi.org/10.1007/s10955-004-8828-y