One-point functions in integrable coupled minimal models

We propose exact vacuum expectation values of local fields for a quantum group restriction of the $C_2^{(1)}$ affine Toda theory which corresponds to two coupled minimal models. The central charge of the unperturbed models ranges from $c=1$ to $c=2$, where the perturbed models correspond to two magnetically coupled Ising models and Heisenberg spin ladders, respectively. As an application, in the massive phase we deduce the leading term of the asymptotics of the two-point correlation functions.