arXiv subjects

D. S. Dean

Publications and source records attributed to D. S. Dean.

43 records · Page 3Linked to original sources

arXiv2001

Tapping Thermodynamics of the One Dimensional Ising Model

We analyse the steady state regime of a one dimensional Ising model under a tapping dynamics recently introduced by analogy with the dynamics of mechanically perturbed granular media. The idea that the steady state regime may be described by a flat measure over metastable states of fixed energy is tested by comparing various steady state time averaged quantities in extensive numerical simulations with the corresponding ensemble averages computed analytically with this flat measure. The agreement between the two averages is excellent in all the cases examined, showing that a static approach is capable of predicting certain measurable properties of the steady state regime.

cond-mat.stat-mech↗

arXiv2000

The Effect of Helicity on the Effective Diffusivity for Incompressible Random Flows

The advection of a passive scalar by a quenched (frozen) incompressible velocity field is studied by extensive high precision numerical simulation and various approximation schemes. We show that second order self consistent perturbation theory, in the absence of helicity, perfectly predicts the effective diffusivity of a tracer particle in such a field. In the presence of helicity in the flow simulations reveal an unexpectedly strong enhancement of the effective diffusivity which is highly nonperturbative and is most visible when the bare molecular diffusivity of the particle is small. We develop and analyse a series of approximation schemes which indicate that this enhancement of the diffusivity is due to a novel second order effect whereby the helical component of the field, which does not directly renormalize the effective diffusivity, enhances the strength of the non helical part of the flow, which in turn renormalizes the molecular diffusivity. We show that this renormalization is most important at low bare molecular diffusivity, in agreement with the numerical simulations.

cond-mat.dis-nn↗

arXiv1999

Metastable states of spin glasses on random thin graphs

In this paper we calculate the mean number of metastable states for spin glasses on so called random thin graphs with couplings taken from a symmetric binary distribution $\pm J$. Thin graphs are graphs where the local connectivity of each site is fixed to some value $c$. As in totally connected mean field models we find that the number of metastable states increases exponentially with the system size. Furthermore we find that the average number of metastable states decreases as $c$ in agreement with previous studies showing that finite connectivity corrections of order $1/c$ increase the number of metastable states with respect to the totally connected mean field limit. We also prove that the average number of metastable states in the limit $c\to\infty$ is finite and converges to the average number of metastable states in the Sherrington-Kirkpatrick model. An annealed calculation for the number of metastable states $N_{MS}(E)$ of energy $E$ is also carried out giving a lower bound on the ground state energy of these spin glasses. For small $c$ one may obtain analytic expressions for $ $.

cond-mat.dis-nn↗

arXiv1997

Boundary Effects in the One Dimensional Coulomb Gas

We use the functional integral technique of Edwards and Lenard to solve the statistical mechanics of a one dimensional Coulomb gas with boundary interactions leading to surface charging. The theory examined is a one dimensional model for a soap film. Finite size effects and the phenomenon of charge regulation are studied. We also discuss the pressure of disjunction for such a film. Even in the absence of boundary potentials we find that the presence of a surface affects the physics in finite systems. In general we find that in the presence of a boundary potential the long distance disjoining pressure is positive but may become negative at closer interplane separations. This is in accordance with the attractive forces seen at close separations in colloidal and soap film experiments and with three dimensional calculations beyond mean field. Finally our exact results are compared with the predictions of the corresponding Poisson-Boltzmann theory which is often used in the context of colloidal and thin liquid film systems.

cond-mat.stat-mech↗

arXiv1996

Renormalization of Drift and Diffusivity in Random Gradient Flows

We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends linearly on the gradient of a gaussian random field with homogeneous statistics. The theoretical analysis is confirmed by numerical simulation. For the purely isotropic case the simulation, which measures the effective drift directly in a constant gradient background field, confirms the result previously obtained theoretically, that the effective diffusivity and effective drift are renormalized by the same factor from their local values. For this isotropic case we provide an intuitive explanation, based on a {\it spatial} average of local drift, for the renormalization of the effective drift parameter relative to its local value. We also investigate situations in which the isotropy is broken by the tensorial relationship of the local drift to the gradient of the random field. We find that the numerical simulation confirms a relatively simple renormalization group calculation for the effective diffusivity and drift tensors.

cond-mat↗

arXiv1995

On the dynamics of a spherical spin-glass

We carry out an analysis of the effect of a quenched magnetic field on the dynamics of the spherical Sherrington-Kirkpatrick spin-glass model. We show that there is a characteristic time introduced by the presence of the field. Firstly, for times sufficiently small the dynamic scenario of the zero field case - with aging effects - is reproduced. Secondly, for times larger than the characteristic time one sees equilibrium dynamics. This dynamical behaviour is reconciled with the geometry of the energy landscape of the model. We compare this behaviour with experimental observations at a finite applied field.

cond-mat↗

arXiv1994

Aging on Parisi's tree

We present a detailed study of simple `tree' models for off equilibrium dynamics and aging in glassy systems. The simplest tree describes the landscape of a random energy model, whereas multifurcating trees occur in the solution of the Sherrington-Kirkpatrick model. An important ingredient taken from these models is the exponential distribution of deep free-energies, which translate into a power-law distribution of the residence time within metastable `valleys'. These power law distributions have infinite mean in the spin-glass phase and this leads to the aging phenomenon. To each level of the tree are associated an overlap and the exponent of the time distribution. We solve these models for a finite (but arbitrary) number of levels and show that a two level tree accounts very well for many experimental observations (thermoremanent magnetisation, a.c susceptibility, second noise spectrum....). We introduce the idea that the deepest levels of the tree correspond to equilibrium dynamics whereas the upper levels correspond to aging. Temperature cycling experiments suggest that the borderline between the two is temperature dependent. The spin-glass transition corresponds to the temperature at which the uppermost level is put out of equilibrium but is subsequently followed by a sequence of (dynamical) phase transitions corresponding to non equilibrium dynamics within deeper and deeper levels. We tentatively try to relate this `tree' picture to the real space `droplet' model, and speculate on how the final description of spin-glasses might look like.

cond-mat↗