arXiv subjects

Gil Zumbach

Publications and source records attributed to Gil Zumbach.

2 recordsLinked to original sources

arXiv1995

Adaptive coordinate, real-space electronic structure calculations on parallel computers

We present a method for electronic structure calculations that retains all of the advantages of real space and addresses the inherent inefficiency of a regular grid, which has equal precision everywhere. The computations are carried out on a {\em regular} mesh in {\em curvilinear space}, which allows natural and efficient decomposition on parallel computers, and effective use of iterative numerical methods. A novel feature is the use of error analysis to optimize the curvilinear grid for highly inhomogeneous electronic distributions. We report accurate all-electron calculations for H$_2$, O, and O$_{2}$.

cond-mat↗

arXiv1995

Importance of the topological defects for two dimensional phase transitions and their relevance for the renormalization group

For various two dimensional non linear $σ$ models, we present a direct comparison between the $β$ functions computed with the $2+ε$ renormalization group and the $β$ functions measured by Monte Carlo simulations. The theoretical and measured $β$ functions match each other nicely for models with a trivial topology, yet they disagree clearly for models containing topological defects. In these later cases, they are compatible with a phase transition at a finite temperature. This indicates that the global properties of the manifold do matter, in contradiction with the assumption used in the $2+ε$ RG computation.

cond-mat↗