Related papers: Energetics and geometry of excitations in random s…
Recent experiments on two-dimensional (2D) electron systems have found a sharp increase in the effective mass of electrons with decreasing electron density. In an effort to understand this behavior we employ the many-body theory to…
A controversial issue in spin glass theory is whether mean field correctly describes 3-dimensional spin glasses. If it does, how can replica symmetry breaking arise in terms of spin clusters in Euclidean space? Here we argue that there…
We consider a directed polymer of length $L$ in a random medium of space dimension $d=1,2,3$. The statistics of low energy excitations as a function of their size $l$ is numerically evaluated. These excitations can be divided into bulk and…
We consider the effect of droplet excitations in the random first order transition theory of glasses on the configurational entropy. The contribution of these excitations is estimated both at and above the ideal glass transition…
The XY model with quenched random phase shifts is studied by a T=0 finite size defect energy scaling method in 2d and 3d. The defect energy is defined by a change in the boundary conditions from those compatible with the true ground state…
We study the statistics of local energy minima in the configuration space and the energy relaxation due to activated hopping in a system of interacting electrons in a random environment. The distribution of the local minima is exponential,…
We investigate, both analytically and numerically, the behavior of the electron gas on a sphere in the presence of point-like impurities. We find a criterion when the disorder can be regarded as small one and the main effect is the…
We investigate numerically disorder chaos in spin glasses, i.e. the sensitivity of the ground state to small changes of the random couplings. Our study focuses on the Edwards-Anderson model in d=1,2,3 and in mean-field. We find that in all…
Theoretical analyses of the random energy model with only two states and its extension with a hierarchy of only two levels show that these models reproduce out-of-equilibrium phenomena observed in experiments of glassy materials; the…
The nature of the spin glass state is investigated by studying changes to the ground state when a weak perturbation is applied to the bulk of the system. We consider short range models in three and four dimensions and the infinite range…
A theory is developed for the evolution of the non-equilibrium distribution of quasiparticles when the scattering rate decreases due to particle collisions. We propose a "modified one-collision approximation" which is most effective for…
We numerically extract large-scale excitations above the ground state in the 3-dimensional Edwards-Anderson spin glass with Gaussian couplings. We find that associated energies are O(1), in agreement with the mean field picture. Of further…
This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin…
The impact of a heavier droplet into a deep pool of lighter liquid is investigated using three-dimensional numerical simulations. Unprecedented to any numerical simulations, we demonstrate that the heavier droplets can hang from the surface…
The two-dimensional random-bond Q-state Potts model is studied for Q near 2 via the perturbative renormalisation group to one loop. It is shown that weak disorder induces cross-correlations between the quenched-averages of moments of the…
Using a stochastic algorithm introduced in a previous paper, we study the finite size volume corrections and the fluctuations of the ground state energy in the Sherrington-Kirkpatrick and the Edwards-Anderson models at zero temperature. The…
The nature of defects in amorphous materials, analogous to vacancies and dislocations in crystals, remains elusive. Here we explore their nature in a three-dimensional microscopic model glass-former which describes granular, colloidal,…
We study the problem of the stability of a two-component droplet. The standard solution known from the literature is based on a particular form of the mean field energy functional, in particular on distinction of hard mode and soft mode…
When a strongly disordered system of interacting quantum dipoles is locally excited, the excitation relaxes on some (potentially very long) timescale. We analyze this relaxation process, both for electron glasses with strong Coulomb…
Excitations of disordered systems such as glasses are of fundamental and practical interest but computationally very expensive to solve. Here we introduce a technique for modeling these excitations in an infinite disordered medium with a…