We analyze the Hertz-Moriya-Millis theory of an antiferromagnetic quantum critical point, in the marginal case of two dimensions (d = 2, z = 2). Up to next-to-leading order in the number of components (N ) of the field, we find that logarithmic corrections do not lead to an enhancement of the Landau damping. This is in agreement with a renormalization-group analysis, for arbitrary N . Hence, the logarithmic effects are unable to account for the behavior reportedly observed in inelastic neutron scattering experiments on CeCu6−xAux. We also examine the extended dynamical meanfield treatment (local approximation) of this theory, and find that only subdominant corrections to the Landau damping are obtained within this approximation, in contrast to recent claims.

We study the low temperature phase of the 3D Coulomb glass within a mean field approach which reduces the full problem to an effective single site model with a non-trivial replica structure. We predict a finite glass transition temperature Tc, and a glassy low temperature phase characterized by permanent criticality. The latter is shown to assure the saturation of the Efros-Shklovskii Coulomb gap in the density of states. We find this pseudogap to be universal due to a fixed point in Parisi's flow equations. The latter is given a physical interpretation in terms of a dynamical self-similarity of the system in the long time limit, shedding new light on the concept of effective temperature. From the low temperature solution we infer properties of the hierarchical energy landscape, which we use to make predictions about the master function governing the aging in relaxation experiments.

A nonlinear screening theory is formulated to study the problem of gap formation and its relation to glassy freezing in classical Coulomb glasses. We find that a pseudo-gap ("plasma dip") in a single-particle density of states begins to open already at temperatures comparable to the Coulomb energy. This phenomenon is shown to reflect the emergence of short range correlations in a liquid (plasma) phase, a process which occurs even in the absence of disorder. Glassy ordering emerges when disorder is present, but this occurs only at temperatures roughly an order of magnitude lower. Our result demonstrate that the formation of the "plasma dip" at high temperatures is a process distinct from the formation of the Efros-Shklovskii (ES) pseudo-gap, which in our model emerges only within the glassy phase.The interplay of interactions and disorder remains one of the most important open problems in condensed matter physics. These effects are most dramatic in disordered insulators, where the pioneering work of Efros and Shklovskii (ES) [1] emphasized the fundamental significance of the long-ranged nature of Coulomb interactions. This work presented convincing evidence that at T = 0 a soft "Coulomb gap" emerges in the single-particle density of states (DOS) which, in arbitrary dimension d, reads( 1) ¿From a general point of view this result is quite surprising. It indicates a power-law distribution of excitation energies, i.e. the absence of a characteristic energy scale for excitations above the ground state. Such behavior is common in models with broken continuous symmetry, where it reflects the corresponding Goldstone modes, but is generally not expected in discrete symmetry models, such as the one used by ES. Here, it may reflect unusually strong frustration behavior inherent to Coulomb interactions in presence of disorder.Indeed, the ES model seems to display several glassy features characterized by a large number of meta-stable states and slow relaxation, as clearly seen in many simulations [2,3,4,5], and even in some experiments [7]. Interestingly, a precursor of the gap begins to appear [4,6] already at relatively high temperatures, while glassy ordering emerges only at much lower T . Similar behavior has been identified even in absence of randomness [8]. Is the physics of the Coulomb gap thus related or is it unrelated to the glassy features of the system? The close connection between the two phenomena was recently demonstrated [9] for a mean-field model of interacting disordered electrons in the limit of large coordination, but the issue remains unresolved for Coulomb systems in finite dimensions where the ES theory applies.To address these important issues in a controlled and precise fashion, we make the following observation which is the main physical point of this letter. We stress that the principal ES result -the emergence of a power-law spectrum -is not specific to low dimensions! Its physical origin and its relation to high temperature anomalies can, therefore, be investigated by the theoretical approaches c...

I propose a simple scaling ansatz for the full replica symmetry breaking solution of the Sherrington-Kirkpatrick model in the low energy sector. This solution is shown to become exact in the limit x --> 0, Bx --> infinity of the Parisi replica symmetry breaking scheme parameter . The distribution function of the frozen fields has been known to develop a linear gap at zero temperature. The scaling equations are integrated to find an exact numerical value for the slope of the gap thetaP(x,y)/delta|(y --> 0) = 0.301 046.... I also use the scaling solution to devise an inexpensive numerical procedure for computing finite time scale (x =1) quantities. The entropy, the zero field cooled susceptibility, and the local field distribution function are computed in the low-temperature limit with high precision, barely achievable by currently available methods.