Joerg Schmalian started his talk with a description of classical mayonnaise: when one mixes oil and vinegar, one obtains a rapid phase separation. However, when egg yolk is added, it acts as an emulsifier, and creates new phase boundaries.

Joerg then discussed the experimental motivation for his study of quantum mayonnaise: the glassiness observed in the underdoped region of the cuprate superconductors, as observed by NMR (Borsa, Curro + Hammel, Imai) and muSR (Panagopoulos) experiments, and the non-Fermi-liquid behavior observed above a critical pressure in MnSi by Pfleiderer+ Lohneysen and Lonzarich. The question is thus what is the quantum emulsifier that gives rise to possible phase separation and glassiness, and non-Fermi liquid behavior associated with them.

Joerg introduced the model he considered in order to study phase separation and glassiness in strongly correlated electron system. One introduces a scalar order parameter which is positive (negative) in phase A (B). The Hamiltonian of the system is given by a phi^4-theory with the constraint that the spatial average of the order parameter vanishes. Joerg considered a long-range interaction that decays algebraically in space as x^(-alpha) with alpha being smaller or equal to the dimension of the system. Assuming that alpha=d-2, one finds that the propagator is isotropic and peaked at some characteristic momentum q0. This model is similar to one developed by Brazovskii, which exhibits a fluctuation-induced first order phase transition into a density-wave state.

Joerg then discussed the role of disorder. For disorder given by a random mass term, Joerg argued that a critical disorder strength is required before the first order phase transition is replaced by a transition into a glassy state. He therefore considered random field disorder, for which a glassy state survives even in the limit of vanishing disorder strength. The glass transition is a random first order transition. Joerg studied this transition using three different theoretical approaches: (i) the replica method, (ii) the Schwinger-Keldysh formalism, and (iii) the cloned replicas approach developed By Remi Monnason. Joerg then briefly discussed the cloned replica approach which addresses the issue of self generated randomness. A test, or bias field is added to a system and selects certain metastable configurations. The averaged free energy of such configuration is then averaged over a Boltzmann weigted distribution governed by an effective temperature. All this becomes practicable since this average can again be formulated using replicas. It turns out that  non-ergodic solutions occur even in the limit of infinitesimal coupling to the test field.

Finally, Joerg discussed the role of quantum fluctuations on the transition into the glassy state and showed that the glassy state melts due to quantum fluctuations. For z<3, the random first order transition into the glass state becomes a (regular) first order transition (with a non-zero latent heat) above a critical fluctuation strength. Joerg derived the RG-flow equations in the limit z->3 which possess an unstable fixed point that corresponds to a tricritical point with new scaling properties. Close to the fixed point the system is in a new non-Fermi liquid state. C/T scales as 1/T^[(z-1)/z] and the imaginary part of the self-energy scales as omega^[(z-1)/z]. This model is therefore one example to obtain hyperscaling and non-fermi liquid physics in 3 space dimensions without deviating from the standard spin-boson coupling.