相关论文: Statistical mechanics of the lattice sphere packin…
It is shown, by means of Monte Carlo simulation and Finite Size Scaling analysis, that the Heisenberg spin glass undergoes a finite-temperature phase transition in three dimensions. There is a single critical temperature, at which both a…
Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest, as they are related to important…
The classical sphere packing problem asks for the best (infinite) arrangement of non-overlapping unit balls which cover as much space as possible. We define a generalized version of the problem, where we allow each ball a limited amount of…
We study statistical and structural properties of extreme lattices, which are the local minima in the density landscape of lattice sphere packings, in $d$-dimensional Euclidean space $\mathbb{R}^d$. Specifically, we ascertain the…
We discuss the high density behavior of a system of hard spheres of diameter d on the hypercubic lattice of dimension n, in the limit n -> oo, d -> oo, d/n=delta. The problem is relevant for coding theory. We find a solution to the…
We introduce a parameter space for periodic point sets, given as unions of $m$ translates of point lattices. In it we investigate the behavior of the sphere packing density function and derive sufficient conditions for local optimality.…
One of the basic problems in discrete geometry is to determine the most efficient packing of congruent replicas of a given convex set $K$ in the plane or in space. The most commonly used measure of efficiency is density. Several types of…
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through…
The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. This problem finds applications…
One of the most significant drawbacks of the all-electron ab initio diffusion Monte Carlo (DMC) is that its computational cost drastically increases with the atomic number ($Z$), which typically scales with $Z^{\sim 6}$. In this study, we…
We perform simulations for long hard-sphere polymer chains using a recently developed binary-tree based Monte Carlo method. Systems in two to five dimensions with free and periodic boundary conditions and up to $10^7$ repeat units are…
We algorithmically characterize the maximal contact number problem for finite congruent lattice sphere packings in $\mathbb{R}^d$ and show that in $\mathbb{R}^3$ this problem is equivalent to determining the maximal coordination of a…
1) We present new lattice sphere packings in Euclid spaces of many dimensions in the range 3332-4096, which are denser than known densest Mrodell-Weil lattice sphere packings in these dimensions. Moreover it is proved that if there were…
In the context of Monte Carlo sampling for lattice models, the complexity of the energy landscape often leads to Markov chains being trapped in local optima, thereby increasing the correlation between samples and reducing sampling…
We define three-point bounds for sphere packing that refine the linear programming bound, and we compute these bounds numerically using semidefinite programming by choosing a truncation radius for the three-point function. As a result, we…
We present here the systematic development of quantitative lattice simulations of dense polymers through a novel computational technique that allows for an efficient accounting of the chain conformations. Our approach is based on the…
We use specialized Monte Carlo simulation methods and moment free energy calculations to provide conclusive evidence that dense polydisperse spheres at equilibrium demix into coexisting fcc phases, with more phases appearing as the spread…
We investigate the problem of packing identical hard objects on regular lattices in d dimensions. Restricting configuration space to parallel alignment of the objects, we study the densest packing at a given aspect ratio X. For rectangles…
The densest local packings of N identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained using a nonlinear programming method operating in conjunction with a stochastic search of…
This review paper is devoted to the problems of sphere packings in 4 dimensions. The main goal is to find reasonable approaches for solutions to problems related to densest sphere packings in 4-dimensional Euclidean space. We consider two…