Critical behavior of frustrated systems: Monte Carlo simulations versus Renormalization Group

We study the critical behavior of frustrated systems by means of Pade-Borel resummed three-loop renormalization-group expansions and numerical Monte Carlo simulations. Amazingly, for six-component spins where the transition is second order, both approaches disagree. This unusual situation is analyzed both from the point of view of the convergence of the resummed series and from the possible relevance of non perturbative effects.Comment: RevTex, 10 pages, 3 Postscript figure

Reaction Networks For Interstellar Chemical Modelling: Improvements and Challenges

We survey the current situation regarding chemical modelling of the synthesis of molecules in the interstellar medium. The present state of knowledge concerning the rate coefficients and their uncertainties for the major gas-phase processes -- ion-neutral reactions, neutral-neutral reactions, radiative association, and dissociative recombination -- is reviewed. Emphasis is placed on those reactions that have been identified, by sensitivity analyses, as 'crucial' in determining the predicted abundances of the species observed in the interstellar medium. These sensitivity analyses have been carried out for gas-phase models of three representative, molecule-rich, astronomical sources: the cold dense molecular clouds TMC-1 and L134N, and the expanding circumstellar envelope IRC +10216. Our review has led to the proposal of new values and uncertainties for the rate coefficients of many of the key reactions. The impact of these new data on the predicted abundances in TMC-1 and L134N is reported. Interstellar dust particles also influence the observed abundances of molecules in the interstellar medium. Their role is included in gas-grain, as distinct from gas-phase only, models. We review the methods for incorporating both accretion onto, and reactions on, the surfaces of grains in such models, as well as describing some recent experimental efforts to simulate and examine relevant processes in the laboratory. These efforts include experiments on the surface-catalysed recombination of hydrogen atoms, on chemical processing on and in the ices that are known to exist on the surface of interstellar grains, and on desorption processes, which may enable species formed on grains to return to the gas-phase.Comment: Accepted for publication in Space Science Review

Translation and validation of the French Movement Imagery Questionnaire. Revised Second Version (MIQ-RS)

Introduction Motor imagery can be defined as a dynamic state during which the representation of a movement is internally rehearsed in the absence of voluntary movements. There are two strategies to mentally simulate the movements, either a visual representation of the movements (visual imagery), or kinesthetic feeling of the movement (kinetic imagery). In stroke rehabilitation, studies indicate that motor imagery associated with physical therapy results in cortical reorganization and correlative functional improvements. Aim The aim of this study is to provide to the French-speaking community a valid and reliable version of the Movement Imagery Questionnaire – Revised Second Version (MIQ-RS). Method We examined the test-retest, inter-rate reliability and the internal consistency of the visual and kinesthetic items of our French version of MIQ-RS in 153 healthy subjects. Results Results showed the internal consistency (Cronbach α = 0.90) and test-retest reliability (intraclass correlation coefficient for visual items = 0.68 and for kinesthetic items = 0.78) of the French version of MIQ-RS were satisfactory; the two-factor structure was supported by confirmatory factor analysis. Conclusion The French version of MIQ-RS is a valid and reliable instrument in French-speaking population and therefore useful as a measure for motor imagery ability

Phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice in applied magnetic field

The Heisenberg antiferromagnet on a two-dimensional triangular lattice is a paradigmatic problem in frustrated magnetism. Even in the classical limit, its properties are far from simple. The "120 degree" ground state favoured by the frustrated antiferromagnetic interactions contains a hidden chiral symmetry, and supports two distinct types of excitation. And famously, three distinct phases, including a collinear one-third magnetisation plateau, are stabilised by thermal fluctuations in applied magnetic field. The questions of symmetry-breaking raised by this model are deep and subtle, and after more than thirty years of study, many of the details of its phase diagram remain surprisingly obscure. In this paper we use modern Monte Carlo simulation techniques to determine the finite-temperature phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice in applied magnetic field. At low to intermediate values of magnetic field, we find evidence for a continuous phase transition from the paramagnet into the collinear one-third magnetisation plateau, belonging to the three-state Potts universality class. We also find evidence for conventional Berezinskii-Kosterlitz-Thouless transitions from the one-third magnetisation plateau into the canted "Y-state", and into the 2:1 canted phase found at high fields. However, the phase transition from the paramagnet into the 2:1 canted phase, while continuous, does not appear to fall into any conventional universality class. We argue that this, like the chiral phase transition discussed in zero field, deserves further study as an interesting example of a finite-temperature phase transition with compound order-parameter symmetry. We comment on the relevance of these results for experiments on magnetic materials with a triangular lattice.Comment: 15 pages, 12 figures, very minor change

Review of important reactions for the nitrogen chemistry in the interstellar medium

Predictions of astrochemical models depend strongly on the reaction rate coefficients used in the simulations. We reviewed a number of key reactions for the chemistry of nitrogen-bearing species in the dense interstellar medium and proposed new reaction rate coefficients for those reactions. The details of the reviews are given in the form of a datasheet associated with each reaction. The new recommended rate coefficients are given with an uncertainty and a temperature range of validity and will be included in KIDA (http://kida.obs.u-bordeaux1.fr).Comment: 39 pages, not published in refereed journal, datasheets are given in KID

Critical thermodynamics of three-dimensional chiral model for N > 3

The critical behavior of the three-dimensional $N$-vector chiral model is studied for arbitrary $N$. The known six-loop renormalization-group (RG) expansions are resummed using the Borel transformation combined with the conformal mapping and Pad\'e approximant techniques. Analyzing the fixed point location and the structure of RG flows, it is found that two marginal values of $N$ exist which separate domains of continuous chiral phase transitions $N > N_{c1}$ and $N N > N_{c2}$ where such transitions are first-order. Our calculations yield $N_{c1} = 6.4(4)$ and $N_{c2} = 5.7(3)$. For $N > N_{c1}$ the structure of RG flows is identical to that given by the $\epsilon$ and 1/N expansions with the chiral fixed point being a stable node. For $N < N_{c2}$ the chiral fixed point turns out to be a focus having no generic relation to the stable fixed point seen at small $\epsilon$ and large $N$. In this domain, containing the physical values $N = 2$ and $N = 3$, phase trajectories approach the fixed point in a spiral-like manner giving rise to unusual crossover regimes which may imitate varying (scattered) critical exponents seen in numerous physical and computer experiments.Comment: 12 pages, 3 figure

Chiral phase transitions: focus driven critical behavior in systems with planar and vector ordering

The fixed point that governs the critical behavior of magnets described by the $N$-vector chiral model under the physical values of $N$ ($N =2, 3$) is shown to be a stable focus both in two and three dimensions. Robust evidence in favor of this conclusion is obtained within the five-loop and six-loop renormalization-group analysis in fixed dimension. The spiral-like approach of the chiral fixed point results in unusual crossover and near-critical regimes that may imitate varying critical exponents seen in physical and computer experiments.Comment: 4 pages, 5 figures. Discussion enlarge

Landau Expansion for the Kugel-Khomskii t2gt_{2g} Hamiltonian

The Kugel-Khomskii (KK) Hamiltonian for the titanates describes spin and orbital superexchange interactions between $d^1$ ions in an ideal perovskite structure in which the three $t_{2g}$ orbitals are degenerate in energy and electron hopping is constrained by cubic site symmetry. In this paper we implement a variational approach to mean-field theory in which each site, $i$, has its own $n \times n$ single-site density matrix \rhov(i), where $n$, the number of allowed single-particle states, is 6 (3 orbital times 2 spin states). The variational free energy from this 35 parameter density matrix is shown to exhibit the unusual symmetries noted previously which lead to a wavevector-dependent susceptibility for spins in $\alpha$ orbitals which is dispersionless in the $q_\alpha$-direction. Thus, for the cubic KK model itself, mean-field theory does not provide wavevector `selection', in agreement with rigorous symmetry arguments. We consider the effect of including various perturbations. When spin-orbit interactions are introduced, the susceptibility has dispersion in all directions in ${\bf q}$-space, but the resulting antiferromagnetic mean-field state is degenerate with respect to global rotation of the staggered spin, implying that the spin-wave spectrum is gapless. This possibly surprising conclusion is also consistent with rigorous symmetry arguments. When next-nearest-neighbor hopping is included, staggered moments of all orbitals appear, but the sum of these moments is zero, yielding an exotic state with long-range order without long-range spin order. The effect of a Hund's rule coupling of sufficient strength is to produce a state with orbital order.Comment: 20 pages, 5 figures, submitted to Phys. Rev. B (2003

Chiral critical behavior in two dimensions from five-loop renormalization-group expansions

We analyse the critical behavior of two-dimensional N-vector spin systems with noncollinear order within the five-loop renormalization-group approximation. The structure of the RG flow is studied for different N leading to the conclusion that the chiral fixed point governing the critical behavior of physical systems with N = 2 and N = 3 does not coincide with that given by the 1/N expansion. We show that the stable chiral fixed point for $N \le N^*$, including N = 2 and N = 3, turns out to be a focus. We give a complete characterization of the critical behavior controlled by this fixed point, also evaluating the subleading crossover exponents. The spiral-like approach of the chiral fixed point is argued to give rise to unusual crossover and near-critical regimes that may imitate varying critical exponents seen in numerous physical and computer experiments.Comment: 17 pages, 12 figure

Field-Induced Two-Step Phase Transitions in the Singlet Ground State Triangular Antiferromagnet CsFeBr3_3

The ground state of the stacked triangular antiferromagnet CsFeBr$_3$ is a spin singlet due to the large single ion anisotropy $D(S^z)^2$. The field-induced magnetic ordering in this compound was investigated by the magnetic susceptibility, the magnetization process and specific heat measurements for an external field parallel to the $c$-axis. Unexpectedly, two phase transitions were observed in the magnetic field $H$ higher than 3 T. The phase diagram for temperature versus magnetic field was obtained. The mechanism leading to the successive phase transitions is discussed.Comment: 8 pages, 9 figures, 10 eps files, jpsj styl