A hard-sphere model on generalized Bethe lattices: dynamics

Hard-sphere-like dynamics in a non-hard-sphere liquid.

The collective dynamics of liquid gallium close to the melting point has been studied using inelastic x-ray scattering to probe length scales smaller than the size of the first coordination shell. Although the structural properties of this partially covalent liquid strongly deviate from a simple hard-sphere model, the dynamics, as reflected in the quasielastic scattering, are beautifully descri...

A percolating hard sphere model

Given a homogeneous Poisson point process in R, Häggström and Meester [2] asked whether it is possible to place spheres (of differing radii) centred at the points, in a translation-invariant way, so that the spheres do not overlap but there is an unbounded component of touching spheres. We prove that the answer is yes in sufficiently high dimension.

Spin systems on hypercubic Bethe lattices: A Bethe-Peierls approach

We study spin systems on Bethe lattices constructed from ddimensional hypercubes. Although these lattices are not tree-like, and therefore closer to real cubic lattices than Bethe lattices or regular random graphs, one can still use the Bethe-Peierls method to derive exact equations for the magnetization and other thermodynamic quantities. We compute phase diagrams for ferromagnetic Ising model...

Dynamics of hard-sphere suspensions.

Glass models on Bethe lattices

We consider " lattice glass models " in which each site can be occupied by at most one particle, and any particle may have at most ℓ occupied nearest neighbors. Using the cavity method for locally tree-like lattices, we derive the phase diagram, with a particular focus on the vitreous phase and the highest packing limit. We also study the energy landscape via the configurational entropy, and di...