Polarized Raman, IR and time-domain THz spectroscopy of orthorhombic lead zirconate single crystals yielded a comprehensive picture of temperature-dependent quasiharmonic frequencies of its low-frequency phonon modes. It is argued that these modes primarily involve vibration of Pb and/or oxygen octahedra librations and their relation to particular phonon modes of the parent cubic phase is proposed. Counts of the observed IR and Raman active modes belonging to distinct irreducible representations agree quite well with group-theory predictions. The most remarkable finding is the considerably enhanced frequency renormalization of the y-polarized polar modes, resulting in a pronounced low temperature dielectric anisotropy. Results are discussed in terms of contemporary phenomenological theory of antiferroelectricity.PACS numbers: 77.80.Bh, 77.84.Cg Although the ferroelectric and antiferroelectric materials have a lot in common, the latter have been much less investigated. An obvious reason is the absence of the direct linear coupling of the antiferroelectric (AF) order parameter to the macroscopic electric field.At the same time, a nonlinear coupling to the macroscopic electric field is still present. Therefore, AF materials actually do provide interesting functionalities, as well. In fact, the AF oxides are promising materials for high-energy storage capacitors, high-strain actuators and perhaps even for electrocaloric refrigerators [1][2][3]. The interest in the improvement of our understanding of AF oxides has been expressed recently [1,2,4,5].Lead zirconate, PbZrO 3 , is the best known example of an AF oxide -it is an end-member of technologically relevant solid solutions with PbTiO 3 (piezoelectric PZTs) [1,2,4,[6][7][8]. The parent paraelectric phase is a simple cubic perovskite with a 5-atom unit cell (P m3m, Z=1). Below the AF phase transition (T C ∼ 500 K), it goes over into an orthorhombic P bam (Z=8) structure [10,11]. The space-group symmetry change can be well understood[1] as a result of the condensation of two order parameters [1,4,9,12]. One of them is a polarization wave of a propagation vector Q Σ = (0.25, 0.25, 0) pc , the other order parameter is a Q R = (0.5, 0.5, 0.5) pc oxygen octahedra tilt mode (here pc stands for pseudocubic lattice, see Figs. 1-2).Superpositions of Q Σ , Q R include also Γ, X, M and Q S = (0.25, 0.25, 0.5) pc cubic-phase Brillouin zone points. All of these points become Brillouin zone centers in the P bam phase (see Fig. 2). Nevertheless, recent inelastic X-ray scattering experiments [4] have clearly demonstrated that the critical scattering occurs only in the vicinity of the Γ-point. Based on this experimental result, it was proposed that the AF phase transition is driven by a single mode, the Γ-point ferroelectric soft mode [4]. Within this model, the condensation of the Q Σ -point mode can be ascribed to the flexoelectric coupling with the ferroelectric mode, and the condensation of the Q R -point mode can be explained as due to a biquadratic coupling with the Q Σ m...

We analyze the replica-symmetry-breaking construction in the Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for deriving an exact asymptotic behavior near the critical temperature of the solution with an arbitrary number of discrete hierarchies of the broken replica symmetry. We show that all solutions with finitely many hierarchies are unstable and only the scheme with infinitely many hierarchies becomes marginally stable. We show how the solutions from the discrete replica-symmetry-breaking scheme go over to the continuous one with increasing number of hierarchies.

A two-particle self-consistency is rarely part of mean-field theories. It is, however, essential for avoiding spurious critical transitions and unphysical behavior. We present a general scheme for constructing analytically controllable approximations with self-consistent equations for the twoparticle vertices based on the parquet equations. We explain in details how to reduce the full set of parquet equations not to miss quantum criticality in strong coupling. We further introduce a decoupling of convolutions of the dynamical variables in the Bethe-Salpeter equations to make them analytically solvable. We connect the self-energy with the two-particle vertices to satisfy the Ward identity and the Schwinger-Dyson equation. We discuss the role of the one-particle self-consistency in making the approximations reliable in the whole spectrum of the input parameters. We demonstrate the general construction on the simplest static approximation that we apply to the Kondo behavior of the single-impurity Anderson model.