Symmetry considerations and a direct, Hubbard-Stratonovich type, derivation are used to construct a replica field-theory relevant to the study of the spin glass transition of short range models in a magnetic field. A mean-field treatment reveals that two different types of transitions exist, whenever the replica number n is kept larger than zero. The Sherrington-Kirkpatrick critical point in zero magnetic field between the paramagnet and replica magnet (a replica symmetric phase with a nonzero spin glass order parameter) separates from the de Almeida-Thouless line, along which replica symmetry breaking occurs. We argue that for studying the de Almeida-Thouless transition around the upper critical dimension d = 6, it is necessary to use the generic cubic model with all the three bare masses and eight cubic couplings. The critical role n may play is also emphasized. To make perturbative calculations feasible, a new representation of the cubic interaction is introduced. To illustrate the method, we compute the masses in one-loop order. Some technical details and a list of vertex rules are presented to help future renormalisation-group calculations.

We study the transition of short range Ising spin glasses in a magnetic field, within a general replica symmetric field theory, which contains three masses and eight cubic couplings, that is defined in terms of the fields representing the replicon, anomalous and longitudinal modes. We discuss the symmetry of the theory in the limit of replica number n → 0, and consider the regular case where the longitudinal and anomalous masses remain degenerate. The spin glass transitions in zero and non-zero field are analyzed in a common framework. The mean field treatment shows the usual results, that is a transition in zero field, where all the modes become critical, and a transition in nonzero field, at the de Almeida-Thouless (AT) line, with only the replicon mode critical. Renormalization group methods are used to study the critical behavior, to order ε = 6 − d. In the general theory we find a stable fixed-point associated to the spin glass transition in zero field. This fixed-point becomes unstable in the presence of a small magnetic field, and we calculate crossover exponents, which we relate to zero-field critical exponents. In a finite magnetic field, we find no physical stable fixed-point to describe the AT transition, in agreement with previous results of other authors.

PACS. 75.10 -General theory and models of magnetic ordering. PACS. 75.105 -Heisenberg and other quantized localized spin models. PACS. 75.40 -Critical-point effects, specific heats, short-range order.

The transverse dynamics of a one-dimensional vector spin glass at zero temperature is treated by a new transfer-matrix scaling technique, and also by evaluating static critical properties related to dynamics by a crossover argument. A nontrivial dynamic exponent is found which implies that the system at zero temperature has dynamic critical behavior w~k, in contradiction to the hydrodynamic behavior normally assumed and to the results of previous work. w ck.By virtue of the divergence of g there is however a possibility that the "velocity" c becomes "critical" near the transition (cf. critical slowing and mode softening at simple continuous thermal ' or geometric2 transitions) in which case (1) has to be replaced by the more general dy-

We study the persistent current and the Drude weight of a system of spinless fermions, with repulsive interactions and a hopping impurity, on a mesoscopic ring pierced by a magnetic flux, using a Density Matrix Renormalization Group algorithm for complex fields. Both the Luttinger Liquid (LL) and the Charge Density Wave (CDW) phases of the system are considered. Under a Jordan-Wigner transformation, the system is equivalent to a spin-1/2 XXZ chain with a weakened exchange coupling. We find that the persistent current changes from an algebraic to an exponential decay 1 as the system crosses from the LL to the CDW phase, with increasing interaction U . We also find that in the interacting system the persistent current is invariant under the impurity transformation ρ → 1/ρ, for large system sizes, where ρ is the defect strength. The persistent current exhibits a scaling behaviour that is in agreement with the scaling behaviour obtained for the Drude weight. We find that in the LL phase the Drude weight scales with the number of lattice sites N as D ∼ N −α , with α > 0 due to the interplay of the electron interaction with the impurity, while in the CDW phase it scales as D ∼ N −δ exp(−N/ξ), ξ being a localization length and δ an exponent which both decrease with increasing interaction and impurity strength. Our results show that disorder and interactions always decrease the persistent current, and imply that the Drude weight vanishes in the limit N → ∞, in both phases.