This review is based on a talk by the authors at the field Scientific session of the Physical Sciences Division of the Russian Academy of Sciences devoted to the 60th anniversary of the Vereshchagin Institute for High Pressure Physics of the Russian Academy of Sciences. The dependence of phase-diagram characteristics and phase transitions on the shape of the intermolecular potential is reviewed and analyzed for two- and three-dimensional systems with isotropic interaction. First, the case of monotonic repulsive and attractive parts of the potential is considered. In particular, it is demonstrated that if the width of the attractive part decreases, the critical point can disappear and even go under the melting curve. In the main part of the review, three-dimensional systems with potentials having a negative curvature in the repulsive region, that is, with two spatial scales in this region, are discussed in detail: in this case, a number of crystalline phases can occur, as can maxima on the melting curve, water-like anomalies, and liquid–liquid transitions. The dependence of the melting scenario on the shape of the potential in two-dimensional systems is also discussed.

We present a molecular dynamics simulation study of the phase diagram and melting scenarios of two-dimensional Hertzian spheres with exponent 7/2. We have found multiple re-entrant melting of a single crystal with a triangular lattice in a wide range of densities from 0.5 to 10.0. Depending on the position on the phase diagram, the triangular crystal has been shown to melt through both twostage melting with a first-order hexatic -isotropic liquid transition and a continuous solid -hexatic transition as well as in accordance with the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKTHNY) scenario (two continuous transitions with an intermediate hexatic phase). We studied the behavior of heat capacity and have shown that despite two-stage melting, the heat capacity has one peak which seems to correspond to a solid-hexatic transition.

We report on the associated production of charmed hadrons in-nucleon interactions at p s 26 GeV at the CERN 0 spectrometer. Results on the azimuthal correlation of charmed particle pairs are presented and compared to the predictions of Next-to-Leading-Order QCD calculations.