Histogram Monte Carlo study of multicritical behavior in the hexagonal easy-axis Heisenberg antiferromagnet

The results of a detailed histogram Monte-Carlo study of critical-fluctuation effects on the magnetic-field temperature phase diagram associated with the hexagonal Heisenberg antiferromagnet with weak axial anisotropy are reported. The multiphase point where three lines of continuous transitions merge at the spin-flop boundary exhibits a structure consistent with scaling theory but without the usual umbilicus as found in the case of a bicritical point.Comment: 7 pages (RevTex 3.0), 1 figure available upon request, CRPS-93-1

Nonperturbative renormalization group approach to frustrated magnets

This article is devoted to the study of the critical properties of classical XY and Heisenberg frustrated magnets in three dimensions. We first analyze the experimental and numerical situations. We show that the unusual behaviors encountered in these systems, typically nonuniversal scaling, are hardly compatible with the hypothesis of a second order phase transition. We then review the various perturbative and early nonperturbative approaches used to investigate these systems. We argue that none of them provides a completely satisfactory description of the three-dimensional critical behavior. We then recall the principles of the nonperturbative approach - the effective average action method - that we have used to investigate the physics of frustrated magnets. First, we recall the treatment of the unfrustrated - O(N) - case with this method. This allows to introduce its technical aspects. Then, we show how this method unables to clarify most of the problems encountered in the previous theoretical descriptions of frustrated magnets. Firstly, we get an explanation of the long-standing mismatch between different perturbative approaches which consists in a nonperturbative mechanism of annihilation of fixed points between two and three dimensions. Secondly, we get a coherent picture of the physics of frustrated magnets in qualitative and (semi-) quantitative agreement with the numerical and experimental results. The central feature that emerges from our approach is the existence of scaling behaviors without fixed or pseudo-fixed point and that relies on a slowing-down of the renormalization group flow in a whole region in the coupling constants space. This phenomenon allows to explain the occurence of generic weak first order behaviors and to understand the absence of universality in the critical behavior of frustrated magnets.Comment: 58 pages, 15 PS figure

Heterogeneous photocatalysis of Cr(VI) in the presence of citric acid over TiO2 particles : relevance of Cr(V)-citrate complexes

International audienceTiO2-photocatalytic reduction experiments of Cr(VI) (0.8 mM) under near UV (366 nm) irradiation in the presence of citric acid (0 ≤ [citric acid] (mM) ≤ 40) were performed at pH 2 under air bubbling. Addition of citric acid facilitates Cr(VI) reduction, hindering the electron-shuttle mechanism taking place in pure water. TOC monotonously decreases until all Cr(VI) was reduced. The maximum rate of Cr(VI) reduction was attained for an initial citric acid/Cr(VI) molar ratio, R, equal to 1.25, a further increment in R being detrimental; however, Cr(VI) decay in the presence of citric acid was always faster than in its absence. Cr(VI) reduction takes place through Cr(V) species, readily complexed by citrate and detected by EPR spectroscopy. Quantitative EPR determinations indicate that an important fraction (nearly 15%) of the reduced Cr(VI) is transformed to Cr(V)-Cit, which also undergoes a photocatalytic transformation. The detrimental effect taking place at high conversions for R > 1.25 can be ascribed to secondary steps, i.e., the competition between Cr(VI) and Cr(V) complexes for conduction band electrons or to the competition of Cr(V)-Cit and Cit for holes