  We 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.
