  In this paper we consider a system of spins that consists of two
configurations $\vsi^1,\vsi^2\in\Sigma_N=\{-1,+1\}^N$ with Gaussian
Hamiltonians $H_N^1(\vsi^1)$ and $H_N^2(\vsi^2)$ correspondingly, and these
configurations are coupled on the set where their overlap is fixed
$\{R_{1,2}=N^{-1}\sum_{i=1}^N \sigma_i^1\sigma_i^2 = u_N\}.$ We prove the
existence of the thermodynamic limit of the free energy of this system given
that $\lim_{N\to\infty}u_N = u\in[-1,1]$ and give the analogue of the
Aizenman-Sims-Starr variational principle that describes this limit via random
overlap structures.
