Quasi-long range order in the random anisotropy Heisenberg model

The large distance behaviors of the random field and random anisotropy Heisenberg models are studied with the functional renormalization group in $4-\epsilon$ dimensions. The random anisotropy model is found to have a phase with the infinite correlation radius at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law $<{\bf m}({\bf r}_1) {\bf m}({\bf r}_2)>\sim| {\bf r}_1-{\bf r}_2|^{-0.62\epsilon}$. The magnetic susceptibility diverges at low fields as $\chi\sim H^{-1+0.15\epsilon}$. In the random field model the correlation radius is found to be finite at the arbitrarily weak disorder.Comment: 4 pages, REVTe

Critical behavior of a fluid in a disordered porous matrix: An Ornstein-Zernike approach

Using a liquid-state approach based on Ornstein-Zernike equations, we study the behavior of a fluid inside a porous disordered matrix near the liquid-gas critical point.The results obtained within various standard approximation schemes such as lowest-order $\gamma$-ordering and the mean-spherical approximation suggest that the critical behavior is closely related to that of the random-field Ising model (RFIM).Comment: 10 pages, revtex, to appear in Physical Review Letter

Quasi-long-range order in the random anisotropy Heisenberg model: functional renormalization group in 4-\epsilon dimensions

The large distance behaviors of the random field and random anisotropy O(N) models are studied with the functional renormalization group in 4-\epsilon dimensions. The random anisotropy Heisenberg (N=3) model is found to have a phase with the infinite correlation radius at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law < m(x) m(y) >\sim |x-y|^{-0.62\epsilon}. The magnetic susceptibility diverges at low fields as \chi \sim H^{-1+0.15\epsilon}. In the random field O(N) model the correlation radius is found to be finite at the arbitrarily weak disorder for any N>3. The random field case is studied with a new simple method, based on a rigorous inequality. This approach allows one to avoid the integration of the functional renormalization group equations.Comment: 12 pages, RevTeX; a minor change in the list of reference

Ideal Bose Einstein condensation and disorder effects

Ideal Bose Einstein condensation is studied as a cooperative phase transition for arbitrary dimensionality. The correspondence with the n → ∞ limit of the n-vector model in the constant volume case and with the n = — 2 limit in the constant pressure case is discussed and precised. The influence of a special type of disorder (random sources and sinks) is studied ; a sharp phase transition occurs with new critical exponents which are calculated and shown to violate some scaling laws.La condensation de Bose Einstein, considérée comme une transition de phase, est étudiée dans un espace de dimension arbitraire. La correspondance, avec la limite n → ∞ du modèle n-vecteur pour la condensation à volume constant et avec la limite n = — 2 pour la condensation à pression constante, est discutée et précisée. L'influence d'un type particulier de désordre (sources et puits de bosons aléatoires) est étudiée ; la transition de phase subsiste, avec de nouveaux exposants critiques qui ne satisfont pas certaines lois d'échelle

Propriétés magnétiques des nitrures mixtes de vanadium et de chrome VxCr1-x N

For the FCC nitrides of the first transition series, a discontinuity exists between vanadium nitride which is a paramagnetic metal, and chromium nitride which is an antiferromagnet, and most probably an insulator when pure. The study of the magnetic properties of mixed VN-CrN alloys reveals on one side, for chromium rich alloys, a magnetic phase which is identical to the magnetic phase for CrN, on the other side, for vanadium rich alloys (between 30 and 50 % chromium) another phase which might be a magnetic glass, in which chromium atoms do not show long range magnetic ordering. Complex phenomena show up in between, around the V0,25Cr0,75N composition, which could be interpreted in terms of an ordering of metallic atoms.Pour les nitrures CFC de la première série de transition, une discontinuité apparaît entre le nitrure de vanadium, qui est un métal paramagnétique et le nitrure de chrome, qui est antiferromagnétique et sans doute isolant à l'état pur. L'étude du magnétisme des nitrures mixtes VN-CrN montre, d'une part pour les alliages riches en chrome une phase magnétique identique à celle qui apparaît en dessous de la température ambiante pour CrN, d'autre part pour les alliages riches en vanadium (30 à 50 % de chrome) une autre phase qui pourrait être un verre magnétique, dans lequel les atomes de chrome ne s'organisent pas à grande distance. Des phénomènes complexes apparaissent entre ces deux domaines au voisinage de la composition V 0,75Cr0,25N qui pourraient s'interpréter à partir d'un ordre des atomes métalliques