Related papers: Lindemann melting criterion in two dimensions
We report the specific heat $c_N$ around the melting transition(s) of micrometer-sized superparamagnetic particles confined in two dimensions, calculated from fluctuations of positions and internal energy, and corresponding Monte Carlo…
The melting of elemental solids is modelled as a dislocation-mediated transition on a lattice. Statistical mechanics of linear defects is used to obtain a new relation between melting temperature, crystal structure, atomic volume, and shear…
The two-dimensional steady-state Boltzmann equation for hard-disk molecules in the presence of a temperature gradient has been solved explicitly to second order in density and the temperature gradient. The two-dimensional equation of state…
In the framework of melting as a dislocation-mediated phase transition we derive an equation for the pressure dependence of the melting temperatures of the elements valid up to pressures of order their ambient bulk moduli. Melting curves…
We perform molecular dynamics and Monte Carlo simulations of two-dimensional melting with dipole-dipole interactions. Both static and dynamic behaviors are examined. In the isotropic liquid phase, the bond orientational correlation length 6…
We study the influence of quenched disorder on the two-dimensional melting behavior by using both video-microscopy of superparamagnetic colloidal particles and computer simulations of repulsive parallel dipoles. Quenched disorder is…
According to the Kosterlitz-Thouless-Theory two-dimensional solid films melt by the unbinding of dislocation pairs. A model including quenched random impurities was already studied by Nelson [Phys. Rev. B 27 (1983) 2902], who predicted a…
We report the observation of the transition from an ordered solid-like phase to a disordered liquid-like phase of a lattice of spikes on a ferrofluid surface submitted to horizontal sinusoidal vibrations. The melting transition occurs for a…
Analyzing three approximate methods to locate liquid-solid coexistence in simple systems, an observation is made that all of them predict the same functional dependence of the temperature on density at freezing and melting of the…
In the paper, we investigate the nonlinear thermoelasticity model in two- and three-dimensional convex and bounded domains. We propose new boundary conditions for the displacement. These conditions are not usual in thermoelasticity.…
We present a theory of the melting of elemental solids as a dislocation-mediated phase transition. We model dislocations near melt as non-interacting closed strings on a lattice. In this framework we derive simple expressions for the…
The melting transition of the five different lattices of a bilayer crystal is studied using the Monte-Carlo technique. We found the surprising result that the square lattice has a substantial larger melting temperature as compared to the…
The dynamics and thermodynamics of melting in two-dimensional Coulomb clusters is revisited using molecular dynamics and Monte Carlo simulations. Several parameters are considered, including the Lindemann index, the largest Lyapunov…
We experimentally investigate the crystallization of a uniformly heated quasi-2D granular fluid as a function of filling fraction. Our experimental results for the Lindemann melting criterion, the radial distribution function, the bond…
We investigate theoretically the crucial r\^{o}le of interstitialcies that trigger the melting of a boundary-free crystal. Based on an interstitialcy model that resembles the $J_1$-$J_2$ model of frustrated antiferromagnets with uniaxial…
We derive exact critical-temperature bounds for the classical ferromagnetic Ising model on two-dimensional periodic tessellations of the plane. For any such tessellation or lattice, the critical temperature is bounded from above by a…
The melting temperature ($T_m$) of a solid is generally determined by the pressure applied to it, or indirectly by its density ($n$) through the equation of state. This remains true even for helium solids\cite{wilk:67}, where quantum…
The melting parameter $\Gamma_m$ of a classical one-component plasma is estimated using a relation between melting temperature, density, shear modulus, and crystal coordination number that follows from our model of dislocation-mediated…
The partition function of two-dimensional solitons in a heat bath of mesons is worked out to one-loop. For temperatures large compared to the meson mass, the free energy is dominated by the meson-soliton bound states and the zero modes, a…
We use super-paramagnetic spherical particles which are arranged in a two-dimensional monolayer at a water/air interface to investigate the crystal to liquid phase transition. According to the KTHNY theory a crystal melts in thermal…