Sine-Gordon/Coulomb Gas Soliton Correlation Functions and an Exact Evaluation of the Kosterlitz-Thouless Critical Exponent

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 $\eta =1/4$ 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 ${\beta }^2=8\pi$, 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.

To appear in J. Stat. Phys., 11 pages

References in corpus (5)

• Exact expectation values of local fields in quantum sine-Gordon model
• Unified Approach to Thermodynamic Bethe Ansatz and Finite Size Corrections for Lattice Models and Field Theories
• Form factors of soliton-creating operators in the sine-Gordon model
• The statistical mechanics of the classical two-dimensional Coulomb gas is exactly solved
• Universality in some classical Coulomb systems of restricted dimension

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• Vanishing conductivity of quantum solitons in polyacetylene
• Duality, Quantum Skyrmions and the Stability of an SO(3) Two-Dimensional Quantum Spin-Glass
• Coulomb Gas and Sine-Gordon Model in Arbitrary Dimension
• Non-singular screw dislocations as the Coulomb gas with smoothed out coupling and the renormalization of the shear modulus
• Thermal soliton correlation functions in theories with a Z(N) symmetry