24 research outputs found
The Glassy Potts Model
We introduce a Potts model with quenched, frustrated disorder, that enjoys of
a gauge symmetry that forbids spontaneous magnetization, and allows the glassy
phase to extend from down to T=0. We study numerical the 4 dimensional
model with states. We show the existence of a glassy phase, and we
characterize it by studying the probability distributions of an order
parameter, the binder cumulant and the divergence of the overlap
susceptibility. We show that the dynamical behavior of the system is
characterized by aging.Comment: 4 pages including 4 (color) ps figures (all on page 4
Continuous RSB mean-field solution of the Potts glass
We investigate the p-state mean-field model of the
Potts glass () below the continuous phase transition to a
glassy phase. We find that apart from a solution with a first hierarchical
level of replica-symmetry breaking (1RSB), locally stable close to the
transition point, there is a continuous full replica-symmetry breaking (FRSB)
solution. The latter is marginally stable and has a higher free energy than the
former. We argue that the true equilibrium is reached only by FRSB, being
globally thermodynamically homogeneous, whereas 1RSB is only locally
homogeneous.Comment: REVTeX4.1, 4 pages, 1 figur
Finite-size scaling at the dynamical transition of the mean-field 10-state Potts glass
We use Monte Carlo simulations to study the static and dynamical properties
of a Potts glass with infinite range Gaussian distributed exchange interactions
for a broad range of temperature and system size up to N=2560 spins. The
results are compatible with a critical divergence of the relaxation time tau at
the theoretically predicted dynamical transition temperature T_D, tau \propto
(T-T_D)^{-\Delta} with Delta \approx 2. For finite N a further power law at
T=T_D is found, tau(T=T_D) \propto N^{z^\star} with z^\star \approx 1.5 and for
T>T_D dynamical finite-size scaling seems to hold. The order parameter
distribution P(q) is qualitatively compatible with the scenario of a first
order glass transition as predicted from one-step replica symmetry breaking
schemes.Comment: 8 pages of Latex, 4 figure
Evidence against a glass transition in the 10-state short range Potts glass
We present the results of Monte Carlo simulations of two different 10-state
Potts glasses with random nearest neighbor interactions on a simple cubic
lattice. In the first model the interactions come from a \pm J distribution and
in the second model from a Gaussian one, and in both cases the first two
moments of the distribution are chosen to be equal to J_0=-1 and Delta J=1. At
low temperatures the spin autocorrelation function for the \pm J model relaxes
in several steps whereas the one for the Gaussian model shows only one. In both
systems the relaxation time increases like an Arrhenius law. Unlike the
infinite range model, there are only very weak finite size effects and there is
no evidence that a dynamical or a static transition exists at a finite
temperature.Comment: 9 pages of Latex, 4 figure
A two-parameter random walk with approximate exponential probability distribution
We study a non-Markovian random walk in dimension 1. It depends on two
parameters eps_r and eps_l, the probabilities to go straight on when walking to
the right, respectively to the left. The position x of the walk after n steps
and the number of reversals of direction k are used to estimate eps_r and
eps_l. We calculate the joint probability distribution p_n(x,k) in closed form
and show that, approximately, it belongs to the exponential family.Comment: 12 pages, updated reference to companion paper cond-mat/060126
One-step replica symmetry breaking solution of the quadrupolar glass model
We consider the quadrupolar glass model with infinite-range random
interaction. Introducing a simple one-step replica symmetry breaking ansatz we
investigate the para-glass continuous (discontinuous) transition which occurs
below (above) a critical value of the quadrupole dimension m*. By using a
mean-field approximation we study the stability of the one-step replica
symmetry breaking solution and show that for m>m* there are two transitions.
The thermodynamic transition is discontinuous but there is no latent heat. At a
higher temperature we find the dynamical or glass transition temperature and
the corresponding discontinuous jump of the order parameter.Comment: 10 pages, 3 figure
Dynamical approach to chains of scatterers
Linear chains of quantum scatterers are studied in the process of
lengthening, which is treated and analysed as a discrete dynamical system
defined over the manifold of scattering matrices. Elementary properties of such
dynamics relate the transport through the chain to the spectral properties of
individual scatterers. For a single-scattering channel case some new light is
shed on known transport properties of disordered and noisy chains, whereas
translationally invariant case can be studied analytically in terms of a simple
deterministic dynamical map. The many-channel case was studied numerically by
examining the statistical properties of scatterers that correspond to a certain
type of transport of the chain i.e. ballistic or (partially) localised.Comment: 16 pages, 7 figure
The Effect of Resonances on Diffusive Scattering
The presence of resonances modifies the passage of light or of electrons
through a disordered medium. We generalize random matrix theory to account for
this effect. Using supersymmetry, we calculate analytically the mean density of
states, and the effective Lagrangean of the generating functional for the
two-point function. We show that the diffusion constant scales with the
effective mean level spacing. The latter exhibits a resonance dip. These facts
allow us to interpret experimental results on light scattering for different
concentrations of resonant scatterers.Comment: 12 pages, 1 Figure, to be published in Physical Review
Classical and Quantum Behavior in Mean-Field Glassy Systems
In this talk I review some recent developments which shed light on the main
connections between structural glasses and mean-field spin glass models with a
discontinuous transition. I also discuss the role of quantum fluctuations on
the dynamical instability found in mean-field spin glasses with a discontinuous
transition. In mean-field models with pairwise interactions in a transverse
field it is shown, in the framework of the static approximation, that such
instability is suppressed at zero temperature.Comment: 9 Pages (including 5 Figures), Revtex, Proceedings of the XIV Sitges
Conference, June 1996 (Barcelona) Spai
Path integral for half-binding potentials as quantum mechanical analog for black hole partition functions
The semi-classical approximation to black hole partition functions is not
well-defined, because the classical action is unbounded and the first variation
of the uncorrected action does not vanish for all variations preserving the
boundary conditions. Both problems can be solved by adding a Hamilton-Jacobi
counterterm. I show that the same problem and solution arises in quantum
mechanics for half-binding potentials.Comment: 6 pages, proceedings contribution to "Path integrals - New Trends and
Perspectives", Dresden, September 200