1. The system of interacting atoms is represented as a union of two subsystems, one of which is a system of atoms, and the other is an auxiliary scalar covariant field, which in the non-relativistic limit is equivalent to a given static interatomic potential of general form. 2. It is shown that the auxiliary field is a superposition of Klein-Gordon-Fock fields, the parameters of which are associated with the singular points of the Fourier transform of the corresponding static interatomic potential. 3. The general form of the relativistic Hamiltonian of a system of interacting atoms with account the auxiliary field degrees of freedom is established. 4. It has been proven that, within the framework of the field picture of interatomic interactions, a system of interacting atoms is thermodynamically equivalent to an ideal gas of quasiparticles. The Hamiltonian of the corresponding quasiparticles has been found. 5. It has been established that field degrees of freedom lead to a divergence in the total energy of a classical relativistic system — analogous to an ultraviolet catastrophe. Quantization of the auxiliary field eliminates this divergence. 6. The existence of temperatures at which the specific heat capacity of a system of quasiparticles diverges has been proven. This indicates phase transitions. 7. It has been established that ``precursors'' of phase transitions exist in the vicinity of phase transformation points. These are analogous to the phenomena of pre-crystallization and pre-melting.