title: Rayleigh approximation to ground state of the Bose and Coulomb glasses.
abstract: Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an analytical approach based on the method of functional equations that allows us to construct the Rayleigh approximation to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Our findings break ground for analytical studies of glassy systems, marking an important step towards understanding their properties.
authors.affiliation: Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.
authors.forename: S D
authors.initials: SD
authors.lastname: Ryan
authors.affiliation: Department of Computer Sciences and Computer Methods, Pedagogical University, ul.Podchorazych 2, Krakow 30-084, Poland.
authors.forename: V
authors.initials: V
authors.lastname: Mityushev
authors.affiliation: Materials Science Division, Argonne National Laboratory, 9700 S. Cass Ave, Argonne, Illinois 60439, USA.
authors.forename: V M
authors.initials: VM
authors.lastname: Vinokur
authors.affiliation: Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.
authors.forename: L
authors.initials: L
authors.lastname: Berlyand