  We consider the system of particles on a finite interval with pair-wise
nearest neighbours interaction and external force. This model was introduced by
Malyshev to study the flow of charged particles on a rigorous mathematical
level. It is a simplified version of a 3-dimensional classical Coulomb gas
model. We study Gibbs distribution at finite positive temperature extending
recent results on the zero temperature case (ground states) with external
force. We derive the asymptotic for the mean and for the variances of the
distances between the neighbouring charges. We prove that depending on the
strength of the external force there are several phase transitions in the local
structure of the configuration of the particles in the limit when the number of
particles goes to infinity.
