Valentin. N. Ryzhov

The melting of two-dimensional systems is a fundamental challenge in condensed matter physics, where topological defects and thermal fluctuations play a key role. This work uses molecular dynamics simulations to investigate the melting of particles interacting via the Gay–Berne potential in the weak anisotropy regime (1.0 ≤ k ≤ 1.2). We demonstrate that the melting mechanism depends critically on the particle aspect ratio. For weak anisotropy (k < 1.15), the system follows a hybrid Bernard–Krauth scenario, featuring a continuous crystal-to-hexatic transition, followed by a first-order hexatic-to-isotropic liquid transition. At k ≥ 1.15, the system switches to the full Berezinskii–Kosterlitz–Thouless–Halperin–Nelson–Young scenario with two continuous Berezinskii–Kosterlitz–Thouless transitions. Introducing binary mixtures of particles with different anisotropies suppresses the first-order transition, stabilizing the continuous melting pathway. Therefore, weak shape anisotropy serves as a fundamental switching parameter governing the universal melting behavior of two-dimensional systems.

We compute the properties of four systems across a broad range of thermodynamic parameters, traversing the Widom delta region. This allows us to trace the structural evolution of a supercritical fluid as its density increases from gas-like to liquid-like values. For the first time, we determine the Widom line for a two-dimensional Lennard-Jones fluid and compare it with its three-dimensional counterpart. Furthermore, we analyze the probability distribution of Voronoi cell volumes and contrast the Voronoi volume of individual particles with the system’s average volume. Finally, we identify universal properties in the behavior of supercritical fluids for the Lennard-Jones system, methanol, and water.

The influence of random disorder on melting in two-dimensional (2D) systems is investigated using computer simulation methods. These processes are primarily described using the Berezinskii–Kosterlitz–Thouless (BKT) phase transition theory, which is applied to 2D systems with continuous symmetry. It is shown that random disorder does not have a significant effect on the melting process if it occurs through two continuous BKT transitions with an intermediate hexatic phase. However, if melting occurs through a single first-order transition, disorder can dramatically change its character. Instead of one transition, two transitions occur: the first is the BKT transition from the crystal to the hexatic phase, while the second is the first-order transition from the hexatic phase to an isotropic liquid.

This study involves molecular dynamics simulations aimed at investigating the crystal structure collapse of graphene, graphite and silicene. It shows that in the case of graphene and graphite, crystal structure collapse is related to the sublimation of the sample. At the same time, when a silicene sample is heated at constant volume, it comes into the liquid–gas two-phase region of the phase diagram. The difference in the crystal structure collapse of graphene and silicene is caused by the differences in the pressure of the liquid–gas–crystal triple point. В данном исследовании проведено моделирование методом молекулярной динамики процесса разрушения кристаллической структуры графена, графита и силицена. Показано, что в случае графена и графита разрушение кристаллической структуры связано с сублимацией образца. В то же время, когда образец силицена нагревается при постоянном объеме, он переходит в двухфазную область фазовой диаграммы жидкость–газ. Разница в разрушении кристаллической структуры графена и силицена вызвана различиями в давлении тройной точки жидкость–газ–кристалл.

Modern theories of melting of two-dimensional systems are discussed that are mainly based on the concepts of the Berezinskii–Kosterlitz–Thouless (BKT) theory of phase transitions in two-dimensional systems with continuous symmetry. Today there exist three basic scenarios of melting of two-dimensional crystals. First of all, this is the Berezinskii–Kosterlitz–Thouless–Halperin–Nelson–Young (BKTHNY) theory, in which two-dimensional crystals are melted through two BKT-type continuous transitions with an intermediate hexatic phase. In this case a first-order phase transition can also occur. The third scenario has recently been proposed by Bernard and Krauth (BK), in which melting can occur through a BKT-type transition; in this case the hexatic phase–isotropic fluid transition is a first-order transition. The review presents a critical analysis of the approaches used to determine the parameters and the type of transition by computer simulation methods.

Modern theories of melting of two-dimensional systems are discussed that are mainly based on the concepts of the Berezinskii–Kosterlitz–Thouless (BKT) theory of phase transitions in two-dimensional systems with continuous symmetry. Today there exist three basic scenarios of melting of two-dimensional crystals. First of all, this is the Berezinskii–Kosterlitz–Thouless–Halperin–Nelson–Young (BKTHNY) theory, in which two-dimensional crystals are melted through two BKT-type continuous transitions with an intermediate hexatic phase. In this case a first-order phase transition can also occur. The third scenario has recently been proposed by Bernard and Krauth (BK), in which melting can occur through a BKT-type transition; in this case the hexatic phase–isotropic fluid transition is a first-order transition. The review presents a critical analysis of the approaches used to determine the parameters and the type of transition by computer simulation methods.

Methanol as a basic liquid and the simplest alcohol is widely used in industry and scientific experiments. However, there are still no reliable data on the thermodynamic properties of methanol at high pressure. Here, we present an experimental and computational study of the thermodynamic properties of liquid methanol under high pressure up to 15 kbar, which significantly exceeds previously reported pressures. A temperature response to a small adiabatic change in pressure has been measured using a piston–cylinder apparatus. We have compared our experimental results with the literature data for lower pressures and NIST approximations. We find that all existing experimental data do not agree with each other and with our experiments. The NIST approximations are mainly based on low pressure data and appear to be unreliable in the high pressure region, giving even qualitatively wrong results. OPLS and COMPASS force field models have been used in the method of molecular dynamics. The agreement of molecular simulation with our experimental data is definitely unsatisfactory, which means that the most common computational models of methanol are not sufficiently good. We hope that these experimental data and approximations will help in developing better computational models.