Anomalous dimensions of high-gradient operators in then-vector model in 2+ε dimensions

The anomalous dimensions of operators with an arbitrary number of gradients are determined for then-vector model ind=2+ dimensions in one-loop order. For those operators which do not vanish ind=2 dimensions all anomalous dimensions can be given explicitly. Among the scalar operators (underO(n) andO(d)) with 2s derivatives there is an operator with the full dimensiony=2(1–s)+(1+s(s–1)/(n–2))+O( ²). Thus similarly as for theQ-matrix model investigated by Kravtsov, Lerner, and Yudson, large positive corrections in one-loop order are obtained for then-vector model. Possible consequences of the corrections are discussed.Dedicated to Professor W. Brenig on the occasion of his 60th birthdayWork supported in part by the Sonderforschungsbereich 123 Stochastic Mathematical Models of the Deutsche Forschungsgemeinschaft     

Inverse participation ratio in 2+ε dimensions

The averaged moments of the eigenfunctions (including the inverse participation ratio) of a particle in a random potential are considered near the mobility edge. The exponents of the power laws are given in an-expansion in one-loop order for ad=2+ dimensional system. The calculation is based on a recent formulation of the mobility edge problem which maps it onto a model of interacting matrices.Work supported in part by the Sonderforschungsbereich 123 (Stochastic Mathematic Models) of the Deutsche Forschungsgemeinschaft     

Lattice dynamics of the high-Tc superconductor La2−xMxCuO4

The phonon dispersion curves, the one-phonon density of states and the specific heat of the high-T_c superconductor La_2−xM_xCuO₄ have been calculated in the framework of a shell model. The zone center frequencies are classified according to their vibrational character and compared with the available IR and Raman data. A slight adjustment of the parameters obtained from the known interaction potentials of oxides with perovskite and rock salt structure yields reasonable agreement with the IR, Raman, specific heat, and inelastic neutron scattering data of the polycrystalline material.     

Critical dynamics of φ2n with random fields in the tree approximation

In the tree approximation, the critical relaxational dynamics of ²ⁿ with quenched random fields is calculated by renormalization near the upper critical dimensiond _u=4+2/(n–1). Although the relation between the characteristic frequency _c q and the wave-numberq is as usual,unusual results are obtained for the asymptotic decay of the order-parameter correlation functionS(q,t).Dedicated to Prof. Dr. W. Döring on the occasion of his 75th birthday     

Critical amplitude ratios of the Baxter–Wu model

A Monte Carlo simulation study of the critical and off-critical behavior of the Baxter–Wu model, which belongs to the universality class of the 4-state Potts model, was performed. We estimate the critical temperature window using known analytical results for the specific heat and magnetization. This helps us to extract reliable values of universal combinations of critical amplitudes with reasonable accuracy. Comparisons with approximate analytical predictions and other numerical results are discussed.     

Shape dynamics in 2 + 1 dimensions

Shape Dynamics is a formulation of General Relativity where refoliation invariance is traded for local spatial conformal invariance. In this paper we explicitly construct Shape Dynamics for a torus universe in 2 + 1 dimensions through a linking gauge theory that ensures dynamical equivalence with General Relativity. The Hamiltonian we obtain is formally a reduced phase space Hamiltonian. The construction of the Shape Dynamics Hamiltonian on higher genus surfaces is not explicitly possible, but we give an explicit expansion of the Shape Dynamics Hamiltonian for large CMC volume. The fact that all local constraints are linear in momenta allows us to quantize these explicitly under a certain assumption on the kinematic Hilbert space, and the quantization problem for Shape Dynamics turns out to be equivalent to reduced phase space quantization. We consider the large CMC-volume asymptotics of conformal transformations of the wave function. We then discuss the similarity of Shape Dynamics on the 2-torus with the explicitly constructible strong gravity Shape Dynamics Hamiltonian in higher dimensions.     

Construction of the two-dimensional sine-Gordon model for β<8π

We present a rigorous renormalization group construction of the two-dimensional massless and massive quantum sine-Gordon models in finite volume for the range 0<<8. We prove analyticity in the coupling constant , which implies the convergence of perturbation theory. The field correlation functions and their generating functional are analyzed and shown to have the short distance asymptotics of the free field theory. In the massive case the bounds are uniform in volume and we also obtain uniform estimates on the long distance decay of correlations.Research supported by NSF Grant PHY-9001178Research supported by the Natural Sciences and Engineering Research Council of Canada     

Critical properties of superconducting Ba1−xKxFe2As2

Magnetisation and magneto-resistance measurements have been carried out on superconducting Ba_1?xK_xFe₂As₂ samples with x = 0.40 and 0.50. From high field magnetization hysteresis measurements carried out in fields up to 16 T at 4.2 K and 20 K, the critical current density has been evaluated using the Bean critical state model. The J_C determined from the high field data is >10⁴ A/cm² at 4.2 K and 5 T. The superconducting transitions were also measured resistively in increasing applied magnetic fields up to 12 T. From the variation of the T_C onset with applied field, dH_C2/dT at T_C was obtained to be ?7.708 T/K and ?5.57 T/K in the samples with x = 0.40 and 0.50.     

Four-loop β-function for the N = 1 and N = 2 supersymmetric non-linear sigma model in two dimensions

A superspace calculation of the four-loop β-function is presented for two-dimensional N= 1,2 supersymmetric non-linear σ-models. It is concluded that besides the one-loop contribution which vanishes on Ricci-flat manifolds, the β-function receives four-loop contributions which do not vanish in the Ricci-flat case. Implications for the superstring are discussed.     

Upper Critical Field of a Two-Band SrFe2 − xNixAs2 Superconductor

JETP Letters - The upper critical field of an iron-based SrFe2 − xNixAs2 superconductor single crystal is measured for the first time in longitudinal and transverse magnetic fields up to 16 T...     

A renormalization result for the intersection local time of lattice random walks ind≧3 dimensions

In this paper we derive some general conditions on stable walks inZ ^d , under which the central limit theorem holds for their normalized intersection local time. In particular, we prove that the process given by the normalized intersection local time of the simple random walk inZ ^d , withd3, is weakly convergent to the standard Brownian motion.BiBoS; SFB 237 Bochum-Essen-Düsseldorf; CERFIM, Locarno.     

Exact results for the Barabási model of human dynamics

Human activity patterns display a bursty dynamics with interevent times following a heavy tailed distribution. This behavior has been recently shown to be rooted in the fact that humans assign their active tasks different priorities, a process that can be modeled as a priority queueing system [A.-L. Barabási, Nature (London) 435, 207 (2005)]. In this Letter we obtain exact results for the Barabási model with two tasks, calculating the priority and waiting time distribution of active tasks. We demonstrate that the model has a singular behavior in the extremal dynamics limit, when the highest priority task is selected first. We find that independently of the selection protocol, the average waiting time is smaller or equal to the number of active tasks, and discuss the asymptotic behavior of the waiting time distribution. These results have important implications for understanding complex systems with extremal dynamics.     

The mass gap of the 2d CPn−1 model in finite volume

The mass gap of the 2d CPⁿ⁻¹ model in finite volume is calculated up to two-loop order in pertubation theory. An estimate for the infinite-volume mass gap is given.     

Critical points of the Bose–Hubbard model with three-body local interaction

Using the density matrix renormalization group method, we study a one-dimensional system of bosons that interact with a local three-body term. We calculate the phase diagram for higher densities, where the Mott insulator lobes are surrounded by the superfluid phase. We also show that the Mott insulator lobes always grow as a function of the density. The critical points of the Kosterlitz–Thouless transitions were determined through the von Neumann block entropy, and its dependence on the density is given by a power law with a negative exponent.     

Spin dynamics in the spin glass phase of Y(Mn1−xAlx)2

Zero field SR has been used to probe spin dynamics in the concentrated spin glass Y(Mn_0.9Al_0.1)₂. The spectra follow a stretched exponential form, G_z(t)=exp(–(t)), with reaching 1/3 as the freezing temperature, T_g=60K, is approached. The evolution of G_z(t) with temperature is suggestive of the behaviour of the spin correlation function found by Ogielski in Monte Carlo simulations of the dynamics of the Ising spin glass model. The SR results are correlated with results previously obtained by inelastic neutron scattering.     

Critical behavior of single crystal CuCr2Se4−x Br x (x=0.25)

The doping of bromine has prominent effect on the transport properties of CuCr₂Se₄, where the conductivity of CuCr₂Se_4?x Br _x changes from metallic behavior with x=0 to semiconductor with x=1. In this work, the critical behavior of single crystal CuCr₂Se_4?x Br _x with x=0.25, which lies at the boundary between the metallic and insulating state, is investigated through the magnetization under high magnetic field. The critical exponents β=0.39±0.03 and γ=1.25±0.05 are obtained by the Kouvel–Fisher method, and δ=4.79±0.01 is generated by the critical iso-thermal analysis. The obtained exponent β is close to the prediction of the three-dimensional (3D) Heisenberg model, while γ approaches that of the 3D-Ising model. Although the bromine doping has prominent effect on the transport behavior, the critical exponents are hardly changed. The obtained results indicate that the ferromagnetism is established through one-dimensional Cr–Se–Cr bonds. However, the nearest-neighbor magnetic interaction belonging to the 3D-Heisenberg model also contributes to the ferromagnetic exchange.