A recent paper on the large-scale structure of the Universe presented evidence for a rectangular three-dimensional lattice of galaxy superclusters and voids, with lattice spacing ∼ 120 M pc, and called for some " hitherto unknown process " to explain it. Here we report that a rectangular three-dimensional lattice of intersecting domain walls, with arbitrary spacing, emerges naturally as a class...

We present a complete and detailed derivation of the finite lattice spacing corrections to staggered fermion matrix elements. Expanding upon arguments of Sharpe, we explicitly implement the Symanzik improvement program demonstrating the absence of order a terms in the Symanzik improved action. We propose a general program to improve fermion operators to remove O(a) corrections from their matrix...

The classical problem of homogenization of elliptic operators in arbitrary domains with periodically oscillating coefficients is considered. As the period goes to zero, an asymptotic analysis of the corresponding sequence of operators is performed with the help of this new method which we call in a natural way the Fourier homogenization method, since it is based on the standard Fourier transfor...

This chapter describes a theory of martensitic microstructure. The theory explains why martensites form microstructure and describes how this microstructure depends, often delicately, on the crystalline symmetry and the lattice parameters. The shape-memory e ect is analyzed with this theory and it is shown that only very special materials { those that satisfy signi cant restrictons on their sym...

We describe several techniques for the calculation of multi-loop integrals and their application to heavy quark current correlators. As new results, we present the fourloop correction to the second and third physical moment in the low-energy expansions of vector, axial-vector and scalar quark current correlators. Using a Ward identity, we obtain the third and fourth moment for the pseudo-scalar...

Supersymmetric extension of the QCD (SQCD) is considered, and the scale dependence of some important parameters, i.e., strong coupling αs and b-quark running mass mb, is studied with the help of three-loop renormalization group equations. Fiveavour QCD is considered as a lowenergy effective theory of SQCD, and two-loop decoupling (threshold) effects are taken into account. Variations in running...

We study Fermi fields defined on tori in the presence of gauge backgrounds carrying non-trivial topology. We show that 2k dimensional field space can alternatively be described by fields over a kdimensional space. This dual description is particularly natural when the background is uniform and abelian. The reduction in number of dimensions carries over to the lattice. The lattice ultraviolet re...

Abstract. This paper is the companion article of [6]. We consider a discrete elliptic equation on the d-dimensional lattice Z with random coefficients A of the simplest type: They are identically distributed and independent from edge to edge. On scales large w. r. t. the lattice spacing (i. e. unity), the solution operator is known to behave like the solution operator of a (continuous) elliptic...

This review focuses on the growth of high-quality (Li1−xFex)OHFeSe single crystals by a hydrothermal method using floating-zone-grown AxFe2−ySe2 (A = K, Rb, and Cs) as precursors. The structure, superconductivity, and magnetic behavior of the obtained crystals are highly influenced by the growth conditions, such as time, temperature, and composition. A phase diagram with temperature against the...

The different techniques available for the accurate measurement of lattice fringe spacings are discussed and their relative merit under different circumstances assessed. The relationship between the lattice fringe spacing and the lattice parameter is further examined for both uniform and chemically inhomogeneous material. The techniques described were also applied to an investigation of carbon ...