## Impurities in Frustrated Magnets

L. Balents

Frustrated magnets exhibit a great richness of behavior. One of the most interesting features is the "cooperative paramagnet" or "spin liquid" regime, in which spins are highly correlated but not ordered. In such a correlated background, impurities can have unusual effects. I will describe a number of interesting problems involving impurities in frustrated magnets, and a few (much fewer) results for such problems.

## Impurity-induced surface instabilities in crystal growth

R. Bausch

The way of spreading of impurities in the interface region of a growing crystal leads to a variety of surface instabilities which initiate different types of pattern formation. In addition to the well-known diffusion-induced Mullins-Sekerka instabilities we find two new instabilities of kinetic origin. The first one is a kind of generalization of the Cahn instability, occurring in grain-boundary motion. The second one is due to drift motions of impurities within a segregation layer at the crystal surface. Each of the instabilities occurs in a velocity window of the growth process which, controlled by the system parameters, appears like a new phase in a non-equilibrium situation.

## Cooperative lengthscales in glass-formers

J.P. Bouchaud

Glasses are often described as a bona fide state of matter. The aim of this talk is to review several ideas, old and new, about what makes glasses so special as a state of matter: glasses are liquids that do not flow, characterized by increasingly cooperative dynamics.

## Fluctuation Forces, Geometry and Shape

T. Emig

Electromagnetic force between neutral bodies are governed
by the coordinated dance of fluctuating charges. The resulting quantum
effects are known as van der Waals, London and Casimir forces. These interactions
appear at the atomic scale as well as between macroscopic bodies. Due
to its topological nature, Casimir forces can be controlled by tailoring
the shapes of the interacting bodies. However, due to the diffraction
of vibrations and the non-additivity of these forces, there is no intuitive
way to tell how the force will change with the object's geometry and shape.

In this talk, I shall give a brief introduction to fluctuation induced
forces, review the recent experimental progeress, and present several
new advances in the theory of Casimir interactions.

## Replica theory for Levy Spin Glasses

A. Engel

Infinite-range spin glasses with Levy-distributed couplings show a freezing transition at low temperature which is rather different from the standard case of the SK model. For any temperature the long tails of the Levy-distribution garantee a certain fraction of bonds strong enough to prevail over the thermal disorder. When approaching the transition temperature from above these strong bonds start to percolate through the whole system. Despite the diverging moments of the local field distribution characteristic for the Levy-distribution the transition can be analyzed by using a variant of the replica method developed for diluted systems and optimization problems and by working at imaginary temperature. The analytical results for the transition temperature are compared to the outcomes of numerical simulations using parallel tempering.

## Strange elasticity of liquid-crystal rubber: critical phases

L. Radzihovsky

A liquid-crystal elastomer is a fascinating new form of soft elastic
matter that is a composite of a conventional crosslinked polymer gel
(rubber) and a fluid liquid-crystal. Such *solid* liquid-crystal
amalgam, quite similarly to its fluid liquid-crystal counterpart can
spontaneously partially break spatial (translational and/or
orientational) symmetries. As a consequence of the associated
Goldstone modes its ordered liquid-crystal states exhibit
an unconventional elasticity characterized by soft modes with
symmetry-enforced strict vanishing of some of the elastic
moduli. Focussing on the nematic phase, I will discuss effects
of thermal fluctuations and network heterogeneity, that lead to {\em
universal} non-Hookean long-scale elasticity, controlled by a nontrivial
fixed point. I will thus show that a nematic liquid-crystal elastomer is
an example of a critical *phase*.

## Statistical Physics of Citations

S. Redner

This talk will begin with basic empirical facts about the network of scientific citations, based on all Physical Review publications from the past 110 years. Intriguingly, the evolution of citations appears to be described by nearly linear preferential attachment. A master equation approach will be presented to characterize the citation distribution and related popularity-driven networks. The conditions that lead to exponential, power-law, or more singular citation distributions will be elucidated for general classes of networks. The citation data of Physical Review also reveals many interesting features that motivate new theoretical models. Finally, the Google page-rank analysis of citations will be applied to find "hidden gems" in Physical Review publications.

## Vortices in a quantum Hall p-wave superconductor - how to identify them in interference experiments

B. Rosenow

I will describe the non-abelian quantum Hall effect at filling \nu=5/2, how its excitations can be understood as vortices of a p-wave superconductor, and why they are non-abelian anyons. I will then focus on proposed interference experiments that can serve as a litmus test for identifying non-abelian anyons, and discuss the influence of a coupling between pinned bulk vortices and edge modes on these experiments.

## The classical and quantum gauge glass in two dimensions

L.H. Tang

The two-dimensional (2D) gauge-glass model describes possible vortex glass behavior in disordered superconducting thin films and more recently has been suggested to be a bose metal at zero temperature under weak quantum fluctuations. We report recent numerical analysis of the ground state and low-lying excited states of the corresponding Coulomb gas problem which exhibits zero-temperature criticality in the classical limit. The power-law decay of the spin-wave stiffness with distance is consistently explained in a renormalized dielectric screening theory of gapless vortex-antivortex pair excitations. For the quantum rotor model with strong random frustration, we show that a phase glass phase, characterized by a finite Edwards-Anderson order parameter and zero compressibility, exists at sufficiently low quantum fluctuations. Transition to the Mott insulator state is studied using QMC methods.

## Ferroelectric Nanostructures and Multiferroic Bulk Systems

S. Trimper

Ferroelectric nanostructures and multiferroic bulk systems are widely discussed due to the broad variety of applications. Mostly the analysis is performed using ab-inito methods. The aim of the present talk is to analyze the behavior of such materials based on a microscopic model. The excitation energy, the associated damping, the polarization and the hysteresis are calculated as function of temperature, defect concentration, size and shape. The softening of the mode is strongly influenced by the kind of doping ions, the surface configuration and the defect composition. Additionally to the studies based on a modified Ising model in a transverse field, a mesoscopic approach is carried out in analogy to the Landau-Lifshitz equation with damp¬ing well known for ferromagnets. The analysis is extended to multiferroic bulk systems, where the magnetic moments interact via the Heisenberg model and the multiferroic coupling term depends on the symmetry. The dielectric function and other dynamic properties are presented.

## Long Range Interactions: A simple view on paradoxes

J. Villain

Textbooks of thermodynamics are often written within the assumption of short range interactions. Actually, on the earth, this is generally correct. In a neutron star, it is not. In the presence of long range interactions, the energy is not proportional to the number of particles. Moreover, the canonical and microcanonical descriptions can give quite different results. In particular, the microcanonical specific heat can be negative. Simple, artificial models with distance-independent interactions can exhibit this strange property or not. In the case of distance-dependent interactions, an extension of the concept of domain wall can sometimes help to understand the physical properties. A short review of physical systems with long range interactions will finally be given.

## Collective dynamic state of insulators with Cooper pairing

V. Vinokur

We investigate collective transport of one- and two-dimensional Josephson junction arrays in the insulating state. We derive current-voltage characteristics and find thermally activated transport at small voltages and sharp voltage transition. In a one-dimensional array, both the activation energy and voltage depinning threshold scale linearly with the size of the sample. In 2D arrays, activation energy scales as logarithm of the size of the sample, while threshold voltage retains linear dependence. Both quantities exhibit a peak as functions of magnetic field resulting from the field modulation of the effective Josephson energy of an elemental junction. We propose that the coherent dynamic state of a Cooper-pairs-insulator is the consequence of the mutual synchronization in a Josephson array. Stability of synchronization with respect to disorder explains striking similarity between the ordered arrays and disordered films near the superconductor-insulator transition. At low temperatures, where the quantization of Josephson phase becomes essential, a coherent synchronized state undergoes a sharp transition into a zero-conductance or superinsulating state.