On correlation functions in the perturbed minimal models M(2,2n+1)

Two-point correlation functions of spin operators in the minimal models ${\cal M}_{p,p'}$ perturbed by the field $Φ_{13}$ are studied in the framework of conformal perturbation theory. The first-order corrections for the structure functions are derived analytically in terms of gamma functions. Together with the exact vacuum expectation values of local operators, this gives the short-distance expansion of the correlation functions. The long-distance behaviors of these correlation functions in the case ${\cal M}_{2,2n+1}$ have been worked out using a form-factor bootstrap approach. The results of numerical calculations demonstrate that the short- and long-distance expansions match at the intermediate distances. Including the descendent operators in the OPE drastically improves the convergency region. The combination of the two methods thus describes the correlation functions at all length scales with good precision.

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