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Register a new userAnderson transitions in three-dimensional disordered systems with randomly varying magnetic flux
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Added by
Kawarabayashi Tohru
Publication date
1998
fields
Physics
and research's language is
English
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The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are considered. We find a critical exponent of $ u=1.45pm0.09$ with random scalar potential. Without it, $ u$ is smaller but increases with the system size and extrapolates within the error bars to a value close to the above. The present results support the conventional classification of universality classes due to symmetry.
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The Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for systems both with and without an additional random scalar potential. We find the critical exponent $ u$ for the localization length to be $1.45 pm 0.09$ with a strong random scalar potential. Without it, the exponent is smaller but increases with the system sizes and extrapolates to the above value within the error bars. These results support the conventional classification of universality classes due to symmetry. Fractal dimensionality of the wave function at the critical point is also estimated by the equation-of-motion method.
We study the Anderson transition for three-dimensional (3D) $N times N times N$ tightly bound cubic lattices where both real and imaginary parts of onsite energies are independent random variables distributed uniformly between $-W/2$ and $W/2$. Such a non-Hermitian analog of the Anderson model is used to describe random-laser medium with local loss and amplification. We employ eigenvalue statistics to search for the Anderson transition. For 25% smallest-modulus complex eigenvalues we find the average ratio $r$ of distances to the first and the second nearest neighbor as a function of $W$. For a given $N$ the function $r(W)$ crosses from $0.72$ to 2/3 with a growing $W$ demonstrating a transition from delocalized to localized states. When plotted at different $N$ all $r(W)$ cross at $W_c = 6.0 pm 0.1$ (in units of nearest neighbor overlap integral) clearly demonstrating the 3D Anderson transition. We find that in the non-Hermitian 2D Anderson model, the transition is replaced by a crossover.
The information theoretic observables entropy (a measure of disorder), excess entropy (a measure of complexity) and multi information are used to analyze ground-state spin configurations for disordered and frustrated model systems in 2D and 3D. For both model systems, ground-state spin configurations can be obtained in polynomial time via exact combinatorial optimization algorithms, which allowed us to study large systems with high numerical accuracy. Both model systems exhibit a continuous transition from an ordered to a disordered ground state as a model parameter is varied. By using the above information theoretic observables it is possible to detect changes in the spatial structure of the ground states as the critical point is approached. It is further possible to quantify the scaling behavior of the information theoretic observables in the vicinity of the critical point. For both model systems considered, the estimates of critical properties for the ground-state phase transitions are in good agreement with existing results reported in the literature.
We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, Stochastic Stability and Overlap Equivalence impose constraints on the moments of the overlap probability densities that can be tested against numerical data. We found small deviations from the Ghirlanda-Guerra predictions, which get smaller as system size increases. We also focus on the shape of the overlap distribution, comparing the numerical data to a mean-field-like prediction in which finite-size effects are taken into account by substituting delta functions with broad peaks
We present results on the first excited states for the random-field Ising model. These are based on an exact algorithm, with which we study the excitation energies and the excitation sizes for two- and three-dimensional random-field Ising systems with a Gaussian distribution of the random fields. Our algorithm is based on an approach of Frontera and Vives which, in some cases, does not yield the true first excited states. Using the corrected algorithm, we find that the order-disorder phase transition for three dimensions is visible via crossings of the excitations-energy curves for different system sizes, while in two-dimensions these crossings converge to zero disorder. Furthermore, we obtain in three dimensions a fractal dimension of the excitations cluster of d_s=2.42(2). We also provide analytical droplet arguments to understand the behavior of the excitation energies for small and large disorder as well as close to the critical point.
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