1,425 research outputs found
Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions
We show that the Kronecker sum of d >= 2 copies of a random one-dimensional
sparse model displays a spectral transition of the type predicted by Anderson,
from absolutely continuous around the center of the band to pure point around
the boundaries. Possible applications to physics and open problems are
discussed briefly.Comment: 19 pages, 1 figure. New version corrects misprints and adds
pertaining reference
Renormalization Group Flow of the Two-Dimensional Hierarchical Coulomb Gas
We consider a quasilinear parabolic differential equation associated with the
renormalization group transformation of the two-dimensional hierarchical
Coulomb system in the limit as the size of the block L goes to 1. We show that
the initial value problem is well defined in a suitable function space and the
solution converges, as t goes to infinity, to one of the countably infinite
equilibrium solutions. The nontrivial equilibrium solution bifurcates from the
trivial one. These solutions are fully described and we provide a complete
analysis of their local and global stability for all values of inverse
temperature. Gallavotti and Nicolo's conjecture on infinite sequence of
``phases transitions'' is also addressed. Our results rule out an intermediate
phase between the plasma and the Kosterlitz-Thouless phases, at least in the
hierarchical model we consider.Comment: 34pages,2figures, to appear in CM
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