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 = ~.
Computer simulation of spin glasses
Abstract For two-and three-dimensional Ising model spin glasses we compute by Monte Carlo both a local order parameter and a nonlocal one, whose “susceptibility” diverges at the freezing temperature. The distribution of effective fields seems to have a shallow minimum at H eff = 0. Symmetric hysteresis loops are found.