<p>The phase transition to the state of a phonon gas with pairwise correlations of interacting phonons with opposite momenta is studied. A method for describing such phonon systems within the framework of the self-consistent field model is developed and their thermodynamic characteristics are calculated. It is shown that a phonon gas with pair correlations can exist in a state of unstable thermodynamic equilibrium. The possibility of experimental observation of a solid in such a phase is discussed.</p>