In experiments the two-dimensional systems are realized mainly on solid substrates which introduce quenched disorder due to some inherent defects. The defects of substrates influence the melting scenario of the systems and have to be taken into account in the interpretation of the experimental results. We present the results of the molecular dynamics simulations of the two dimensional system with the core-softened potential in which a small fraction of the particles is pinned, inducing quenched disorder.The potentials of this type are widely used for the qualitative description of the systems with the water-like anomalies. In our previous publications it was shown that the system demonstrates an anomalous melting scenario: at low densities the system melts through two continuous transition in accordance with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory with the intermediate hexatic phase, while at high densities the conventional first order melting transition takes place. We find that the well-known disorder-induced widening of the hexatic phase occurs at low densities, while at high density part of the phase diagram random pinning transforms the first-order melting into two transitions: the continuous KTHNY-like solid-hexatic transition and first-order hexatic-isotropic liquid transition.
We consider the phase behavior of two-dimensional ($2D$)system of particles with an isotropic core-softened potential introduced in our previous publications. As one can expect from the qualitative consideration for the three dimensional case, the system demonstrates a reentrant-melting transition at low densities along with waterlike anomalies in the fluid phase near the melting maximum. In contrast with the three dimensional case, in two dimensions melting is a continuous two-stage transition in the low density part of the phase diagram with an intermediate hexatic phase corresponding to the…
We find that both continuous and discontinuous hexatic-liquid transitions can happen in the melting of two-dimensional solids of soft-core disks. For three typical model systems, Hertzian, harmonic, and Gaussian-core models, we observe the same scenarios. These systems exhibit reentrant crystallization (melting) with a maximum melting temperature $T_m$ happening at a crossover density $ρ_m$. The hexatic-liquid transition at a density smaller than $ρ_m$ is discontinuous. Liquid and hexatic phases coexist in a density interval, which becomes narrower with increasing temperature and tends to vani…
The random disorder can drastically change the melting scenario of two-dimensional systems and has to be taken into account in the interpretation of the experimental results. We present the results of the molecular dynamics simulations of the two dimensional system with the core-softened potentials with two repulsive steps in which a small fraction of the particles is pinned, inducing quenched disorder. It is shown that without the quenched disorder the system with small repulsive shoulder, which is close in the shape to the soft disks, melts in accordance with the melting scenario proposed in…
Despite about forty years of investigations, the nature of the melting transition in two dimensions is not completely clear. In the framework of the most popular Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young (BKTHNY) theory, 2D systems melt through two continuous Berezinskii-Kosterlitz-Thouless (BKT) transitions with intermediate hexatic phase. The conventional first-order transition is also possible. On the other hand, recently on the basis of computer simulations the new melting scenario was proposed with continuous BKT type solid-hexatic transition and first order hexatic-liquid tra…
We present a comparative computer simulation study of the phase diagrams and anomalous behavior of two-dimensional ($2D$) and quasi-two-dimensional ($q2D$) classical particles interacting with each other through isotropic core-softened potential which is used for a qualitative description of the anomalous behavior of water and some other liquids. We have shown that at the low density part of the phase diagram an increase in the width of the confining slit pore leads to a considerable decrease in the melting temperature while at high densities the melting temperature is almost unchanged.
In the present paper, using a molecular dynamics simulation, we study a nature of melting of a two-dimensional ($2D$) system of classical particles interacting through a purely repulsive isotropic core-softened potential which is used for the qualitative description of the anomalous behavior of water and some other liquids. We show that the melting scenario drastically depends on the potential softness and changes with increasing the width of the smooth repulsive shoulder. While at small width of the repulsive shoulder the melting transition exhibits what appears to be weakly first-order behav…
We present the results of a computer simulation study of the melting scenario of two-dimensional soft-disk systems with potential $U(r)=\varepsilon(σ/r)^n$, $n=12$ and $n=1024$, both in the presence of random pinning and without it. The melting parameters have been determined from analysis of the behavior of equations of state, correlation functions of the orientational and translational order parameters, Young modulus and renormalization group equations. The transition points obtained from these criteria are in good agreement. We have shown that the systems melted in two stages - first-order …
We investigate the structural, thermodynamic and dynamic behavior of of a two dimensional core-corona system using Langevin Dynamics simulations. The particles are modeled using a core-softened potential that exhibits waterlike anomalies for the 3D case. For quasi-2D systems we have observed previously a new region of structural anomaly. Now, our results show that a new region of structural, density and diffusion anomalies arises for the 2D system. Our findings indicates that while the anomalous region at lower densities observed is due the competition between the two length scales in the pote…
2D competitive systems shows a large variety of solid and aggregate patterns, re-entrant fluid phase, a continuous melting as predicted by the KTHNY theory and, in some cases, waterlike anomalies. In this paper, we employ Langevin Dynamics simulations of a ramp-like core-softened fluid that have two characteristic length scales and all the features mentioned above. Analyzing the fluid phase of this system, Bordin and Barbosa [Phys. Rev. E 97, 022604 (2018)] reported the existence of two waterlike anomalous region. Now, we revisit this problem focusing in the low temperature regime and a larger…
A set of interacting vortices in $2D$ in the presence of a substrate with square symmetry and at filling ratio $1$ can display a low temperature solid phase where only one of the reciprocal lattice vectors of the substrate is present\cite{toby1,fasano}. This partially pinned vortex lattice melts to a modulated liquid via a continuous transition \cite{toby1}. Brownian dynamics simulation is carried out to study the behavior of driven partially pinned solid at different temperatures. The average vortex velocity for forces above the depinning threshold shows a non-monotonic behavior with temperat…
Using molecular dynamics simulation we have investigated the influence of random pinning on the phase diagram and melting scenarios of a two-dimensional (2D) system with the Hertz potential for $α=5/2$. For the first time it has been shown that random pinning can cardinally change the mechanism of first-order transition between the different crystalline phases (triangular and square) by virtue of generating hexatic and tetratic phases: a triangular crystal to hexatic transition is of the continuous Berezinskii-Kosterlitz-Thouless (BKT) type, a hexatic to tetratic transition is of the first-ord…
Ultrastable glasses have risen to prominence due to their potentially useful material properties and the tantalizing possibility of a general method of preparation via vapor deposition. Despite the importance of this novel class of amorphous materials, numerical studies have been scarce because achieving ultrastability in atomistic simulations is an enormous challenge. Here we bypass this difficulty and establish that randomly pinning the position of a small fraction of particles inside an equilibrated supercooled liquid generates ultrastable configurations at essentially no numerical cost, wh…
We study the phase behaviour and the collective dynamics of interacting paramagnetic colloids assembled above a honeycomb lattice of triangular shaped magnetic minima. A frustrated colloidal molecular crystal is realized when filling these potential minima with exactly two particles per pinning site. External in-plane rotating fields are used to anneal the system into different phases, including long range ordered stripes, random fully packed loops, labyrinth and disordered states. At higher amplitude of the annealing field, the dimer lattice displays a two step melting transition where the in…
