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arXiv:hep-th/9312207 · Nuclear Physics B

Manifestly finite perturbation theory for the short-distance expansion of correlation functions in the two-dimensional Ising model

Bakhtiar Mikhak, Amir M. Zarkesh

Published Nov 1, 1994• 12 citations
arXivHTMLPDF
DOI
10.1016/0550-3213(94)90164-3

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We propose a new class of universal amplitude ratios which involve the first terms of the short distance expansion of the correlators of a statistical model in the vicinity of a critical point. We will describe the critical system with a conformal field theory (UV fixed point) perturbed by an appropriate relevant operator. In two dimensions the exact knowledge of the UV fixed point allows for accurate predictions of the ratios and in many nontrivial integrable perturbations they can even be evaluated exactly. In three-dimensional O ( N ) scalar systems, feasible extensions of some existing results should allow perturbative expansions for the ratios to be obtained. By construction these universal ratios are a perfect tool to explore the short distance properties of the underlying quantum field theory even in regimes where the correlation length and one-point functions are not accessible in experiments or simulations.
We apply here a recently developed approach to compute the short distance corrections to scaling for the correlators of all primary operators of the critical two dimensional Ising model in a magnetic field. The essence of the method is the fact that if one deals with O.P.E. Wilson coefficients instead of correlators, all order I.R. safe formulas can be obtained for the perturbative expansion with respect to magnetic field. This approach yields in a natural way the expected fractional powers of the magnetic field, that are clearly absent in the naive perturbative expression for correlators. The technique of the Mellin transform have been used to compute the I.R. behavior of the regularized integrals. As a corollary of our results, by comparing the existing numerical data for the lattice model we give an estimate of the Vacuum Expectation Value of the energy operator, left unfixed by usual nonperturbative approaches (Thermodynamic Bethe Ansatz).