This review is based on a talk by the authors at the outdoor 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 form of 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 a repulsive region, that is, with two space scales in this region, are discussed in detail: in this case, a number of crystalline phases may occur, as might maxima on the melting curve, water-like anomalies, and liquid-liquid transitions. The dependence of the melting scenario on the form of the potential in two-dimensional systems is also discussed.
Keywords: theory of liquids, effective potentials, core-softened potentials, liquid anomalies, structural anomaly, diffusion anomaly, density anomaly, two-dimensional systems, melting scenarios, Berezinskii—Kosterlitz—Thouless—Halperin—Nelson—Young theory, Hertz potential, phase diagram PACS:02.70.Ns, 64.10.+h, 64.70.D− (all) DOI:10.3367/UFNe.2018.04.038417 URL: https://ufn.ru/en/articles/2020/5/a/ Citation: Ryzhov V N, Tareyeva E E, Fomin Yu D, Tsiok E N "Complex phase diagrams of systems with isotropic potentials: results of computer simulations" Phys. Usp.63 417–439 (2020)