2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/187179We consider a completely integrable lattice regularization of the sine-Gordon model with discrete space and continuous time. We derive a determinant representation for a correlation function which in the continuum limit turns into the correlation function of local fields. The determinant is then embedded into a system of integrable integro-differential equations. The leading asymptotic behaviour of the correlation function is described in terms of the solution of a Riemann Hilbert Problem (RHP) related to the system of integro-differential equations. The leading term in the asymptotical decomposition of the solution of the RHP is obtained.30 pages Latex2e, 2 Figures, epsf. Significantly extended and revised versionHigh Energy Physics - TheoryCondensed Mattertext