Modelling the gluon propagator

Scaling of the Landau gauge gluon propagator calculated at beta=6.0 and at beta=6.2 is demonstrated. A variety of functional forms for the gluon propagator calculated on a large (32^3x64) lattice at beta=6.0 are investigated.Comment: LATTICE98(confine), 3 pages, 2 figure

Electronic nematicity and its relation to quantum criticality in Sr_3Ru_2O_7 studied by thermal expansion

We report high-resolution measurements of the in-plane thermal expansion anisotropy in the vicinity of the electronic nematic phase in Sr$_3$Ru$_2$O$_7$ down to very low temperatures and in varying magnetic field orientation. For fields applied along the c-direction, a clear second-order phase transition is found at the nematic phase, with critical behavior compatible with the two-dimensional Ising universality class (although this is not fully conclusive). Measurements in a slightly tilted magnetic field reveal a broken four-fold in-plane rotational symmetry, not only within the nematic phase, but extending towards slightly larger fields. We also analyze the universal scaling behavior expected for a metamagnetic quantum critical point, which is realized outside the nematic region. The contours of the magnetostriction suggest a relation between quantum criticality and the nematic phase.Comment: 8 pages, 12 Figures, invited paper at QCNP 2012 conferenc

Symmetry-breaking lattice distortion in Sr_3Ru_2O_7

The electronic nematic phase of Sr$_3$Ru$_2$O$_7$ is investigated by high-resolution in-plane thermal expansion measurements in magnetic fields close to 8 T applied at various angles $\Theta$ off the c-axis. At $\Theta<10^\circ$ we observe a very small ($10^{-7}$) lattice distortion which breaks the four-fold in-plane symmetry, resulting in nematic domains with interchanged $a$- and b-axis. At $\Theta \gtrsim 10^\circ$ the domains are almost fully aligned and thermal expansion indicates an area-preserving lattice distortion of order $2\times 10^{-6}$ which is likely related to orbital ordering. Since the system is located in the immediate vicinity to a metamagnetic quantum critical end point, the results represent the first observation of a structural relaxation driven by quantum criticality.Comment: 4 pages, 5 figures, PRL accepte

Anisotropy of the low-temperature magnetostriction of Sr3Ru2O7

We use high-resolution capacitive dilatometry to study the low-temperature linear magnetostriction of the bilayer ruthenate Sr$_3$Ru$_2$O$_7$ as a function of magnetic field applied perpendicular to the ruthenium-oxide planes ($B\parallel c$). The relative length change $\Delta L(B)/L$ is detected either parallel or perpendicular to the c-axis close to the metamagnetic region near B=8 T. In both cases, clear peaks in the coefficient $\lambda(B)=d(\Delta L/L)/dB$ at three subsequent metamagnetic transitions are observed. For $\Delta L\perp c$, the third transition at 8.1 T bifurcates at temperatures below 0.5 K. This is ascribed to the effect of an in-plane uniaxial pressure of about 15 bar, unavoidable in the dilatometer, which breaks the original fourfold in-plane symmetry.Comment: 3 pages, 3 Figures, Manuscript for Proceedings of the International Conference on Quantum Criticality and Novel Phases (QCNP09, Dresden

The Gluon Propagator in Momentum Space

We give preliminary numerical results for the gluon propagator evaluated both in coordinate and momentum space on a 16^3X40 quenched lattice at beta=6.0. Our findings are compared with earlier results in the literature at zero momentum. In addition, by considering nonzero momenta we attempt to extract the form of the propagator and compare it to continuum predictions formulated by Gribov and others. latex, file espcrc2.sty needed (appended at the end: search for espcrc2.sty).Comment: 4 page

Uniaxial stress tuning of geometrical frustration in a Kondo lattice

Hexagonal CeRhSn with paramagnetic $4f$ moments on a distorted Kagome lattice displays zero-field quantum critical behavior related to geometrical frustration. We report high-resolution thermal expansion and magnetostriction measurements under multiextreme conditions such as uniaxial stress up to 200 MPa, temperatures down to 0.1 K and magnetic fields up to 10 T. Under uniaxial stress along the $a$-direction, quantum criticality disappears and a complex magnetic phase diagram arises with a sequence of phases below 1.2 K and fields between 0 and 3 T ($\parallel a$). Since the Kondo coupling increases with stress, which alone would stabilize paramagnetic behavior in CeRhSn, the observed order arises from the release of geometrical frustration by in-plane stress.Comment: Accepted in PRB Rapid Com

Deciding Robust Feasibility and Infeasibility Using a Set Containment Approach: An Application to Stationary Passive Gas Network Operations

In this paper we study feasibility and infeasibility of nonlinear two-stage fully adjustable robust feasibility problems with an empty first stage. This is equivalent to deciding whether the uncertainty set is contained within the projection of the feasible region onto the uncertainty-space. Moreover, the considered sets are assumed to be described by polynomials. For answering this question, two very general approaches using methods from polynomial optimization are presented - one for showing feasibility and one for showing infeasibility. The developed methods are approximated through sum of squares polynomials and solved using semidefinite programs. Deciding robust feasibility and infeasibility is important for gas network operations, which is a nonconvex feasibility problem where the feasible set is described by a composition of polynomials with the absolute value function. Concerning the gas network problem, different topologies are considered. It is shown that a tree structured network can be decided exactly using linear programming. Furthermore, a method is presented to reduce a tree network with one additional arc to a single cycle network. In this case, the problem can be decided by eliminating the absolute value functions and solving the resulting linearly many polynomial optimization problems. Lastly, the effectivity of the methods is tested on a variety of small cyclic networks. It turns out that for instances where robust feasibility or infeasibility can be decided successfully, level 2 or level 3 of the Lasserre relaxation hierarchy typically is sufficient