Related papers: Step fluctuations for a faceted crystal
In a recent paper [Ferrari et al., Phys. Rev. E 69, 035102(R) (2004)], the scaling law of the fluctuations of the step limiting a crystal facet has been computed as a function of the facet size. Ferrari et al. use rigorous, but physically…
For 3D geometries, we consider stones (modeled as convex polyhedra) subject to weathering with planar slices of random orientation and depth successively removing material, ultimately yielding smooth and round (i.e. spherical) shapes. An…
Three models from statistical physics can be analyzed by employing space-time determinantal processes: (1) crystal facets, in particular the statistical properties of the facet edge, and equivalently tilings of the plane, (2)…
We consider the shape of crystals which are soft in the sense that their elastic modulus $\mu$ is small compared to their surface tension $\gamma$, more precisely $ \mu a < \gamma$ where $a$ is the lattice spacing. We show that their…
Molecular dynamics (MD) simulations are employed to investigate the capillary fluctuations of steps on the surface of a model metal system. The fluctuation spectrum, characterized by the wave number ($k$) dependence of the mean squared…
The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A…
We devise a geometric description of bounded systems at criticality in any dimension $d$. This is achieved by altering the flat metric with a space dependent scale factor $\gamma(x)$, $x$ belonging to a general bounded domain $\Omega$.…
A model in statistical mechanics, characterised by the corresponding Gibbs measure, is a subset of the totality of probability distributions on the phase space. The shape of this subset, i.e., the geometry, then plays an important role in…
The problem addressed here can be concisely formulated as follows: given a stable surface orientation with a known reconstruction and given a direction in the plane of this surface, find the atomic structure of the steps oriented along that…
Cracks develop various surface patterns as they propagate in three-dimensional (3D) materials. Facet formation in nominally tensile (mode-I) fracture emerge in the slow, non-inertial regime and oftentimes takes the form of surface steps. We…
It is experimentally observed that adsorbate atoms and vacancies on (111) surfaces of fcc metals cluster into islands which are approximately hexagonal, but which on closer inspection turn out to have equilibrium facets which alternate in…
We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Sch\"{u}tz-type formula is derived for the transition probability. We investigate an…
The stability of a discrete time crystal against thermal fluctuations has been studied numerically by solving a stochastic Landau-Lifshitz-Gilbert equation of a periodically-driven classical system composed of interacting spins, each of…
A theory for the thermodynamic properties of steps on faceted crystalline surfaces is presented. The formalism leads to the definition of step excess quantities, including an excess step stress that is the step analogy of surface stress.…
We consider both equilibrium and kinetic aspects of the phase separation (``thermal faceting") of thermodynamically unstable crystal surfaces into a hill--valley structure. The model we study is an Ising lattice gas for a simple cubic…
For low to moderate supersaturations, crystals grow by lateral build-up of new layers. The edges of the layers are known as "steps". We consider the rate of step advance on a flat crystal face under the influence of bulk diffusion in the…
For stationary, homogeneous Markov processes (viz., L\'{e}vy processes, including Brownian motion) in dimension $d\geq 3$, we establish an exact formula for the average number of $(d-1)$-dimensional facets that can be defined by $d$ points…
Nuclear matter at large number of colors is necessarily in a solid phase. In particular holographic nuclear matter takes the form of a crystal of instantons of the flavor group. In this article we initiate the analysis of the…
We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be…
Synthetic dimension platforms offer unique pathways for engineering quantum matter. We compute the phase diagram of a many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as a…