  It is shown that the Josephson subsystem of the Lawrence-Doniach model of
layered superconductors in the London approximation can be presented as a
system with variable number of classical Coulomb particles. This allows us to
consider the vortex system of a coupled layered superconductor as the system of
these particles and 2D-vortices interacting with each other. The grand
partition function of the system was written and transformed into the form of
field one. Thermodynamical properties of the model obtained was studied. It is
found that there is no a phase transition in the system. Instead of this the
model demonstrates the crossover from a low temperature 3D behavior to high
temperature 2D one which can look as a phase transition for experimental
purposes.
