Related papers: On the low-dimensional solids and their melting
In contrast to three-dimensional (3D) crystals that melt via a first-order transition, two-dimensional (2D) crystals can exhibit various melting scenarios under different temperatures, pressures, and particle interactions, particularly when…
We present an extensive but concise review of our present understanding, largely based on theory and simulation work from our group, on the equilibrium behavior of solid surfaces and nanosystems close to the bulk melting point. In the first…
We elucidate the interplay between diverse two-dimensional melting pathways and establish solid/hexatic and hexatic/liquid transition criteria via the numerical simulations of the melting transition of two- and three-component mixtures of…
Melting in two spatial dimensions, as realized in thin films or at interfaces, represents one of the most fascinating phase transitions in nature, but it remains poorly understood. Even for the fundamental hard-disk model, the melting…
We perform extensive simulations of $10^4$ Lennard-Jones particles to study the effect of particle size dispersity on the thermodynamic stability of two-dimensional solids. We find a novel phase diagram in the dispersity-density parameter…
Some soliton equation in 2+1 dimensions and their 1+1 and/or dimensional integrable reductions are considered.
We study 2D solids with weak substrate disorder, using Coulomb gas renormalisation. The melting transition is found to be replaced by a sharp crossover between a high $T$ liquid with thermally induced dislocations, and a low $T$ glassy…
We demonstrate that particles confined to two dimensions (2d) and subjected to a one-dimensional (1d) periodic potential exhibit a rich phase diagram, with both ``locked floating solids'' and smectic phases. The resulting phases and phase…
Melting and freezing transitions in two dimensional systems are known to show highly unusual characteristics. Most of the earlier studies considered atomic systems; the melting behavior in two dimensional molecular solids is still largely…
There are strong evidences that the melting in two dimensions depends crucially on the form and range of the interaction potentials between particles. We study with Monte Carlo simulations the phase diagram and the melting of a monolayer of…
The "melting" of self-formed rigid structures made of a small number of interacting classical particles confined in an irregular two-dimensional space is investigated using Monte Carlo simulations. It is shown that the interplay of…
It is demonstrated that the Lindemann's criterion of melting can be formulated for two-dimensional classical solids using statistical mechanics arguments. With this formulation the expressions for the melting temperature are equivalent in…
We investigate the behaviour of dipolar bosons in two dimensions. We describe the large density crystalline limit analytically while we use quantum Monte-Carlo to study the melting toward the Bose-Einstein condensate. We find strong…
In this paper a model for partial melts is constructed using two-scale homogenization theory. While this technique is well known to the mathematics and materials communities, it is relatively novel to problems in the solid Earth. This…
Amorphous solids at low temperature display unusual features which have been escaped a clear and unified comprehension. In recent years a mean field theory of amorphous solids constructed in the limit of infinite spatial dimensions has been…
The melting transitions of a colloidal lattice confined to a two-dimensional ($2D$) periodic substrate of square symmetry are studied using Monte Carlo simulations. When the strengths of interparticle and particle-substrate interactions are…
A brief review is given of some well-known and some very recent results obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered.…
As the dimensionality is reduced, the world becomes more and more interesting; novel and fascinating phenomena show up which call for understanding. Physics in one dimension is a fascinating topic for theory and experiment: for the former…
Amorphous solids show surprisingly universal behaviour at low temperatures. The prevailing wisdom is that this can be explained by the existence of two-state defects within the material. The so-called standard tunneling model has become the…
A pure and incompressible material is confined between two plates such that it is heated from below and cooled from above. When its melting temperature is comprised between these two imposed temperatures, an interface separating liquid and…