Critical behavior in c=1c=1 matrix model with branching interactions

Motivated by understanding the phase structure of $d >1$ strings we investigate the $c=1$ matrix model with g' (\tr M(t)^{2})^{2} interaction which is the simplest approximation of the model expected to describe the critical phenomena of the large-$N$ reduced model of odd-dimensional matrix field theory. We find three distinct phases: (i) an ordinary $c=1$ gravity phase, (ii) a branched polymer phase and (iii) an intermediate phase. Further we can also analyse the one with slightly generalized g^{(2)} (\frac{1}{N}\tr M(t)^{2})^{2} +g^{(3)} (\frac{1}{N}\tr M(t)^{2})^{3} + \cdots + g^{(n)} (\frac{1}{N}\tr M(t)^{2})^{n} interaction. As a result the multi-critical versions of the phase (ii) are found.Comment: 11pages. latex (The arguments in Discussions are corrected and more clarified! Several grammatical errors are corrected. And some preprints in references are replaced with the published versions.

Electronic Structures of Oxygen-deficient Ta2O5

We provide a first-principles description of the crystalline and oxygen-deficient Ta2O5 using refined computational methods and models. By performing calculations on a number of candidate structures, we determined the low-temperature phase and several stable oxygen vacancy configurations, which are notably different from the previous results. The most stable charge-neutral vacancy site induces a shallow level near the bottom of conduction band. Stability of different charge states is studied. Based on the results, we discuss the implications of the level structures on experiments, including the leakage current in Ta2O5-based electronic devices and catalysts.Comment: 23 pages, 4 figures and 2 tables in the body texts plus 4 figures in the supplementary materia