Evidence is accumulating that the electron liquid in the cuprate superconductors is characterized by manyhole correlations of the charged magnetic domain-wall type. Here we focus on the strong-coupling limit where all holes are bound to domain walls. We assert that at high temperatures a classical domain-wall fluid is realized and show that the dynamics of such a fluid is characterized by spatial and temporal crossover scales set by temperature itself. The fundamental parameters of this fluid are such that the domain-wall motions dominate the low-frequency spin fluctuations and we derive predictions for the behavior of the dynamical magnetic susceptibility. We argue that a crossover occurs from a high-temperature classical to a lowtemperature quantum regime, in direct analogy with helium. We discuss some general characteristics of the domain-wall quantum liquid, realized at low temperatures. I. DOMAIN WALLS IN DOPED ANTIFERROMAGNETSSince the discovery of the cuprate superconductors the issue of hole doping in two-dimensional antiferromagnetic insulators has received considerable attention. Especially in the regime of low to moderate doping a number of unusual properties emerge. Here we want to suggest an interpretation of these phenomena in this regime in terms of holes bound to domain walls, separating antiferromagnetic regions -see Fig. 1. Fluctuations prevent these domain walls from freezing into an ordered state and we thus get a spatially and temporally disordered, liquidlike phase of the type sketched in Fig. 2. We associate the dynamics of this liquid state with the anomalous magnetic fluctuations of the cuprates.We are motivated in part by recent studies of the t-J model revealing tendencies towards the formation of such an inhomogeneous state over a large range of parameters.1 It was found, by exact diagonalization of small systems ͑18 -20 sites͒ with four holes, that upon increasing J/t a phase with domain-wall correlations appears before phase separation occurs.2 Earlier, these domain walls were found to be the classical ͑Hartree-Fock͒ saddle points of Hubbard models at finite doping, 3,4 surviving in more sophisticated variational approaches such as the Gutzwiller ansatz 5 and in fixed-node quantum Monte Carlo. 6 We also mention that long-range Coulomb interactions are not as hazardous to this type of ordering as one would expect at first sight. It was recently shown that the mere electrostatics problem, combined with short-range attractive forces already favors the formation of striped charged phases. 7Also some recent experimental developments give support to these domain-wall ideas. As we shall discuss later in more detail, these domain walls have recently been directly observed in doped La 2 NiO 4 , 8 which is a close relative of the cuprates. 9 Indications for the existence of domain walls in lightly doped La 2 CuO 4 were brought forward in the context of magnetic-susceptibility measurements.10 Finally, domain walls were proposed as a possible explanation for the Korringa behavior of the oxygen ...

Abstract. We review the nonlinear a-model approach to the localization problem. However, different from usual, we do not make use of replicas or superfields in order to perform the averaging over the realizations of the disorder. Instead, we pursue the derivation of the nonlinear a-model as an effective theory for the disordered electron system within the framework of the so-called time-path formalism, which is a real-time finite-temperature quantum field theory. This formalism is especially suitable for the description of the disordered electron system due to the automatic normalization of real-time quantities, thereby avoiding the denominator problem. We shall compare this dynamic method with the replica-and superfield-methods as the perturbative level of the calculation of physical quantities.

The emergence of glassy behavior of the random field Ising model (RFIM) is investigated using an extended mean-field theory approach. Using this formulation, systematic corrections to the standard Bragg-Williams theory can be incorporated, leading to the appearance of a glassy phase, in agreement with the results of the self-consistent screening theory of Mezard and Young. Our approach makes it also possible to obtain information about the low temperature behavior of this glassy phase. We present results showing that within our mean-field framework, the hysteresis and avalanche behavior of the RFIM is characterized by power-law distributions, in close analogy with recent results obtained for mean-field spin glass models.

Experimental indications for the role of the van Hove singularity (vHs) in the electronic density of states of high Tc superconductors are discussed. It is argued that (i) like the resistivity, the measured temperature and doping dependences of the normal state electronic specific heat of YBCO are consistent with the existence of a vHs and (ii) the doping dependence of Tc in the underdoped and optimally doped regimes may be accounted for mainly by a vHs. Further, we discuss the suppression of the quasiparticle scattering rate below Tc, and the coherence lengths in the hole-doped materials and NCCO. Assuming that the same mechanism for superconductivity operates in the electron-doped and the hole-doped cuprates, we argue that the bosonic mode that causes the superconductivity is strongly influenced by the doping in the overdoped regime. We further argue that this boson involves an energy scale larger than that of phonons and is only weakly coupled to the charge carriers.