ERRATUM: Disordered spherical model

Disordered spherical bead packs are anisotropic

Investigating how tightly objects pack space is a long-standing problem, with relevance for many disciplines from discrete mathematics to the theory of glasses. Here we report on the fundamental yet so far overlooked geometric property that disordered mono-disperse spherical bead packs have significant local structural anisotropy manifest in the shape of the free space associated with each bead...

A Dynamical Study of the Disordered Quantum p = 2 Spherical Model

Michal Rokni and Premala Chandra Chandra Tech Consulting LLC, 123 Harper Street, Highland Park, NJ 08904 Abstract We present a dynamical study of the disordered quantum p = 2 spherical model at long times. Its phase behavior as a function of spin-bath coupling, strength of quantum fluctuations and temperature is characterized, and we identify different paramagnetic and coarsened regions. A quan...

Erratum

Disordered backgammon model.

In this paper we consider an exactly solvable model that displays glassy behavior at zero temperature due to entropic barriers. The new ingredient of the model is the existence of different energy scales or modes associated with different relaxational time scales. Low-temperature relaxation takes place by partial equilibration of successive lower-energy modes. An adiabatic scaling solution, def...

A spherical Hopfield model

We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynam-ics and dynamics of this model. In order to have a retrieval phase a quartic term is added to the Hamiltonian. The thermodynamics of the model is exactly solvable and the results are replica symmetric. A Langevin dynamics leads to a closed set of equa...