CORRIGENDUM: Phase transition in the two-dimensional frustrated x-y model: scaling equations
The author establishes scaling equations for the two-dimensional x-y model with weak frustration using the electrostatic analogy of Kosterlitz and Thouless. In the limit of small disorder he finds a shift in the critical temperature Tc(x)-Tc(0)=-(Jx/kB)(2 pi 2- pi /2 ln 2x) and the exponents are unchanged from the pure values.
Theory of one- and two-dimensional magnets with an easy magnetization plane. II. The planar, classical, two-dimensional magnet
Résumé. 2014 On donne une nouvelle méthode d’étude des systèmes planaires magnétiques à 2 dimen-sions : le Hamiltonien est remplacé par une approximation qui, contrairement aux approximations antérieures, préserve la symétrie correcte du problème. On confirme l’existence d’une transition à Tc et on donne une évaluation quantitative de Tc et de la fonction de corrélation de paire au-dessous de Tc. Les résultats sont en accord à basse température avec ceux de l’approximation de Hartree. On prévoit une transition à une température KB Tc = 1,7 Js2, en bon accord avec les prédictions des développements en séries à haute température, alors que les exposants critiques sont ceux prévus par Kosterlitz, notamment 03B3 = ~. Abstract. 2014 A new approach to the 2-D classical planar magnet is proposed. The Hamiltonian is replaced by an approximate one, which, in contrast with previous approximations, preserves the correct symmetry of the problem; the existence of a phase transition without long range order at some temperature Tc is confirmed; quantitative evaluations of the spin pair correlation function below Tc, and of the transition temperature Tc are given; the results are in good agreement at low T with the self consistent harmonic approximation (S.C.H.A.). A transition is predicted at a temperature KB Tc = 1.7 Js2, in very good agreement with predictions based on series expansions, whereas the critical exponents are those predicted by Kosterlitz, in particular 03B3 = ~.
An analytical approach to the design of electrodes in high-power, fast-transverse-flow CO2 lasers
Abstract Usually, the design of the electrodes of fast-transverse-flow CO 2 lasers relies more on experimental data than on theoretical analysis. Traditional systems sustain a stable, high-power discharge but the current distribution generates a peaked, non-uniform small-signal-gain pattern. We present a theoretical model suitable for the design of electrodes that achieves a quasi uniform gain distribution. The analysis, based on a two-temperature model and the gas-transport equations, computes the electron density that supports a flat gain pattern. Combining the desired electron density with the electron-balance equations, the model determines the required electric field. The results were used to design a new set of electrodes for a home-made fast transverse flow CO 2 laser. A stable, large volume discharge ( 4 × 8 × 90 cm 3 ) with very good uniformity was obtained. The resulting gain distribution was registered in a bi-dimensional map. The peak gain rose from 1.2 m - 1 , attained with the old electrode set, to 1.6 m - 1 with the new one and the gain showed a homogeneous profile.