Refining glass structure in two dimensions

Dynamic glass transition in two dimensions.

The question of the existence of a structural glass transition in two dimensions is studied using mode coupling theory (MCT). We determine the explicit d dependence of the memory functional of mode coupling for one-component systems. Applied to two dimensions we solve the MCT equations numerically for monodisperse hard disks. A dynamic glass transition is found at a critical packing fraction ph...

Dynamics and structure of a colloidal glass former in two dimensions

Spin glass stiffness in zero dimensions

A unique analytical result for the Migdal–Kadanoff hierarchical lattice is obtained. The scaling of the defect energy for a zero-dimensional spin glass is derived for a bond distribution that is continuous at the origin. The value of the ‘stiffness’ exponent in zero dimensions, y0 = −1, corresponds to the value also found in one dimension. This result complements and completes earlier findings ...

The algebraic structure of geometric flows in two dimensions

There is a common description of different intrinsic geometric flows in two dimensions using Toda field equations associated to continual Lie algebras that incorporate the deformation variable t into their system. The Ricci flow admits zero curvature formulation in terms of an infinite dimensional algebra with Cartan operator ∂/∂t. Likewise, the Calabi flow arises as Toda field equation associa...

Microscopic structure of the metal-insulator transition in two dimensions.

A single electron transistor is used as a local electrostatic probe to study the underlying spatial structure of the metal-insulator transition in two dimensions. The measurements show that as we approach the transition from the metallic side, a new phase emerges that consists of weakly coupled fragments of the two-dimensional system. These fragments consist of localized charge that coexists wi...