Related papers: Step fluctuations for a faceted crystal
Melting behaviors of defective crystals under extreme conditions are theoretically investigated using the statistical moment method. In our theoretical model, heating processes cause missing atoms or vacancies in crystal structures via…
Classical phase transitions, like solid-liquid-gas or order-disorder spin magnetic phases, are all driven by thermal energy fluctuations by varying the temperature. On the other hand, quantum phase transitions happen at absolute zero…
We derive a stochastic process that describes the kinetics of a one-dimensional Bose gas in a regime where three body collisions are important. In this situation the system becomes non integrable offering the possibility to investigate…
We numerically study the finite-size droplet condensation-evaporation transition in two dimensions. We consider and compare two orthogonal approaches, namely at fixed temperature and at fixed density, making use of parallel multicanonical…
The critical point is a fixed point in finite-size scaling. To quantify the behaviour of such a fixed point, we define, at a given temperature and scaling exponent ratio, the width of scaled observables for different sizes. The minimum of…
We study several one dimensional step flow models. Numerical simulations show that the slope of the profile exhibits scaling in all cases. We apply a scaling ansatz to the various step flow models and investigate their long time evolution.…
We simulate structure in the vicinity of different size nanovoids using a new variant of the Molecular Statics, wherein atomic structure in the vicinity of nanovoids and the parameters that define the displacements of atoms placed in…
The Ising model at inverse temperature $\beta$ and zero external field can be obtained via the Fortuin-Kasteleyn (FK) random-cluster model with $q=2$ and density of open edges $p=1-e^{-\beta}$ by assigning spin +1 or -1 to each vertex in…
The geometrical approach to phase transitions is illustrated by simulating the high-temperature representation of the Ising model on a square lattice.
We study the one-dimensional active Ising model in which aligning particles undergo diffusion biased by the signs of their spins. The phase diagram obtained varying the density of particles, their hopping rate and the temperature…
We describe a numerical model of faceted crystal growth using a cellular automata method that incorporates admolecule diffusion on faceted surfaces in addition to bulk diffusion in the medium surrounding the crystal. The model was developed…
The crystallization proceeds by the advance of the crystal faces into the disordered phase at the expense of the supersaturation which is not sustained in our model. Using a conservation constraint for the transformation ratio and a kinetic…
According to the Wulff construction the shape of the equilibrium crystal is determined by the surface tension considered as a function of the interface orientation. We present some (conjectured) approximate solutions and some rigorous…
We show how various mathematical formalisms, specifically the catastrophe formalism and group theory, aid in the study of relevant systems in quantum optics. We describe the phase transition of the Dicke model for a finite number N of…
The relaxation of axisymmetric crystal surfaces with a single facet below the roughening transition is studied via a continuum approach that accounts for step energy g_1 and step-step interaction energy g_3>0. For diffusion-limited…
The simplest statistical-mechanical model of crystalline formation (or alloy formation) that includes electronic degrees of freedom is solved exactly in the limit of large spatial dimensions and infinite interaction strength. The solutions…
In this paper, we present an exactly solvable phase transition model in which the phase transition is purely statistically derived. The phase transition in this model is a generalized Bose-Einstein condensation. The exact expression of the…
We work out an exactly solvable hamiltonian model which retains all the features of realistic quantum measurements. In order to use an interaction process involving a system and an apparatus as a measurement, it is necessary that the…
The present paper formulates and solves a problem of dividing coins. The basic form of the problem seeks the set of the possible ways of dividing coins of face values 1,2,4,8,... between three people. We show that this set possesses a…
We study a crystal growth Markov model proposed by Gates and Westcott (\cite{Kinetics1}, \cite{Kinetics2}). This is an aggregation process where particles are packed in a square lattice accordingly to prescribed deposition rates. This model…