Studies of the ultrarelativistic collisions of hadrons and nuclei at different centrality and energy enable to explore the QCD phase diagram in a wide range of temperature and baryon density. Long-range correlation studies are considered as a tool, sensitive to the observation of phase transition and the critical point. In the present work, a Monte Carlo model of proton-proton, proton-nucleus, and nucleus-nucleus collisions is applied to heavy and light ion collisions at the cms energy range from a few up to several hundred GeV per nucleon. The model describes the nuclear collisions at the partonic level through interaction of color dipoles and takes into account the effects of string fusion, which can be considered as an alternative to relativistic hydrodynamics way of describing the collective phenomena in heavy-ion collisions. The implementing of both the string fusion and the finite rapidity length of strings allowed to consider the particle production at non-zero baryochemical potential. We calculated the long-range correlation functions and correlation coefficients between multiplicities and transverse momentum at several energies for different colliding systems and obtained predictions for the experiment.