Self-avoiding walks on percolation clusters at criticality and lattice animals

We use the real-space renormalization group method to study the critical behavior of self-avoiding walks (SAWs) on both site percolation clusters at percolation threshold and site lattice animals in a square lattice. The correlation length exponents of SAWs are found to be on the percolation clusters atp _c and _SAW ^LA =0.804 on lattice animals. These results are compared with Kremer's suggestion of modified Flory formula where is the fractal dimension of the fractal object.     

The microstructure of electrodeposited amorphous or microcrystalline Fe-P alloys

Dependent on is produced through electrodeposition in three modifications: microcrystalline if , amorphous if and in a mixed state containing both components if . The interpretation of results of large and small angle X-ray scattering, of measurements of the coercivity and of the mechanical density shows that the three modifications consist of two phases. The structure of the grain boundary phase in the microcrystalline alloys differs considerably from that of the amorphous phase. This arises from the dependence of the atomic volume on the average phosphorus content . The volume fraction of the crystalline component decreases with increasing up to . But even in alloys revealing X-ray patterns without any peaks coming from crystalline particles small angle X-ray scattering indicates the existence of metal-rich inclusions occupying some percent of the total volume.     

Evidence for a new Hume-Rothery phase with an amorphous structure

It will be shown that binary amorphous alloys with a noble metal and a polyvalent non-transition element, as constituents, can be described essentially as a Hume-Rothery phase. Some structural as well as transport properties depend on , the average number of the conduction electrons per atom. A strong similarity between the amorphous and the corresponding liquid alloys was found. Alloys of the type mentioned can exist in a homogeneous amorphous phase within a concentration range which is limited on the noble-metal rich side by =1.8 and on the other side by about 20 at% noble-metal content. The influence of the conduction electrons, manifested in the Friedel oscillations of the effective pair potentials, is responsible for structural and electronic transport properties. For amorphous and liquid alloys with =1.8 it is interesting to note thatk _pe , the wave number at which the maximum in the structure factor occurs, is equal to 2k _F , the diameter of the Fermi sphere. As far as we have determined, all amorphous alloys with =1.8 containing the same noble metal have the same crystallization temperature and the same Hall coefficient independent of the polyvalent element. The individual influence of the polyvalent constituents can only be seen with increasing .     

Temperature evolution of the umbrella structure in holmium iron garnet

Using neutron diffraction data, the thermal evolution of the magnetic structure of Ho₃Fe₅O₁₂ has been studied. Below the compensation temperature (T _comp=137 K), the umbrella structure parameters which fit the spontaneous ferrite magnetizations have been determined. AboveT _comp, the compound behaves as a Néel type ferrimagnet. Particular attentions have been given to the magnetic form factors of both iron sublattice on one hand and on the other hand to a rhombohedral distorsion fromI a3d toR below 30 K and in first approximation toR c forT>30 K.     

Recursion method for the density of states and spectral dimension of percolation networks

We use the recursion method to calculate the vibrational density of states of site percolation clusters slightly above the percolation threshold. It is found that is proportional to at long wavelengths. At shorter length scales, is proportional to , with the fraction dimension . The cross-over from phonon to fraction regime is characterized by a rapid rise in in agreement with effective medium calculations.     

Low density flux fluids in high —T c superconductors: The influence of disorder

We analyze the influence of thermal and frozen-in disorder on the flux line (FL) density close to the lower critical fieldH _c1. Arguments which consider the steric repulsion of fluctuating FLs give with the roughness exponent of a single FL andd the space dimensionality. We show by a phenomenological scaling approach and a renormalization group treatment, that this is correct only fordd _c =2/–1, i.e. for . Ford>d _c the steric FL repulsion at scales more than some critical one is irrelevant and . For disordered superconductorsd _c =2 and ford=2, 3. We also found the melting line for a FL lattice in the presence of frozen-in impurities close toH _c1.     

On equivalent-neighbour,random site models of disordered systems

Models of random systems whose Hamiltonian reads , where and _i ,=1,...,n are independent, identically distributed random variables are discussed.J _ij are assumed to be symmetric, with respect toJ ₀, random variables and also symmetric functions of components of . A question of dependence of a phase diagram on a probability distribution of is addressed. A class of distributions and interactionsJ _ij , which give rise to phase diagrams called typical is selected. Then a problem of obtaining typical phase diagrams, containing a certain region with an infinite number of pure phases, is studied.     

Fluctuations of pair correlations and the spin glass transition in amorphous Al2Mn3Si3O12

The time fluctuations of the pair correlations in the amorphous spin glass Al₂Mn₃Si₃O₁₂ were investigated by quasi-elastic neutron scattering. Their time constant follows an Arrhenius law from room temperature down to below the spin glass temperatureT _f. No static component of the pair correlation was found. It is shown that an Arrhenius law can qualitatively account for all the phenomena associated with the ac susceptibility as a function of temperature, ac frequency and applied dc magnetic field.Dedicated to Professor Jagodzinski on the occasion of his 65th birthday     

Dynamics of vector spin glasses with random anisotropy

The dynamics of vector spin glasses with additional random anisotropy is investigated in the mean field approximation. We find a cross-over of the upper critical line from a behaviour of Heisenberg spins with a field-temperature dependence , for large fieldsH, to Ising like behaviourT _f –TT ^2/3 , for small fields and fixed anisotropy, in agreement with results of Kotliar and Sompolinsky. Here, andT _f are characteristic spin glass temperatures. In addition, one has a second line with reversed behaviour which presumably represents a cross-over line from weak to strong non-ergodicity. The local transverse susceptibility _T () varies for large fields and 0 along the upper critical line as ^vT , with a critical exponentV _T = 1/2 – 11D/60 J, whereD andJ are the anisotropy and exchange coupling constants, respectively. On the Ising-like part of the upper critical line one has isotropic spin glass parameters,q _L =q _T , and susceptibilities, and a critical exponent, which is similar to that of Ising spins along the de Almeida-Thouless line.Dedicated to B. Mühlschlegel on the occasion of his 60th birthdaySFB Aachen-Jülich-Köln     

Ensemble and trajectory statistics in a nonlinear partial differential equation

We have examined the influence of parametric noise on the solution behavioru(t, x) of a nonlinear initial value() problem arising in cell kinetics. In terms of ensemble statistics, the eventual limiting solution mean and variance are well-characterized functions of the noise statistics, and and depend on . When noise is continuously present along the trajectory, and are independent of the noise statistics and . However, in their evolution toward and , both _u (t, x) and _u ² (t, x) depend on the noise and.     

Finite elastic coupling effects in critical sound propagation in dilute Ising systems

The nonasymptotic critical properties of sound propagation induced by finite spin-strain coupling are studied in dilute Ising model aboveT _c by means of renormalization group methods and expansion. It is shown that effective hydrodynamic sound attenuation exponent is lower in compressible systems than in the almost rigid ones. Scaling functions for sound attenuation and dispersion are obtained in the crossover region to the first order.     

Entropy functionals of Kolmogorov-Sinai type and their limit theorems

Two functionals and are introduced forC ^*-dynamical systems with invariant states and stationary channels. It is shown that the Kolmogorov-Sinai-type theorems hold for these functionals and . Our functionals and are set within the framework of quantum information theory and generalize a quantum KS entropy by CNT and the mutual entropy by Ohya.     

Superconformal current algebras and their unitary representations

A natural supersymmetric extension is defined of the current (= affine Kac-Moody Lie) algebra ; it corresponds to a superconformal and chiral invariant 2-dimensional quantum field theory (QFT), and hence appears as an ingredient in superstring models. All unitary irreducible positive energy representations of are constructed. They extend to unitary representations of the semidirect sumS (G) of with the superconformal algebra of Neveu-Schwarz, for , or of Ramond, for =0.On leave of absence from the Institute for Nuclear Research and Nuclear Energy of the Bulgarian Academy of Sciences, BG-1184 Sofia, Bulgaria     

Three-hadron form factor via quark-triangle loop

An explicit construction in a manifestly Lorentz-invariant and cyclically symmetric form is given for a three-hadron (H) coupling through their respective (q ) constituents interacting via a quark triangle loop under the most general conditions of unequal mass kinematics atboth the elementary quark and composite-hadron levels. The only ansatz employed is that theHq vertex function _H at each vertexi is a function of _i , the relative momentumtransverse to the corresponding hadron momentumP _i, an assumption which can be justified from several independent angles. The resulting structure , withD( ) being a model-independent function, has proved crucial for an explicit integration over the time-like component of the loop momentum, and thus provided an analytical, cyclically symmetric structure free of overlapping pole singularities. The applicational potential of this quantity is outlined.     

On the purification of factor states

Let be aC*-algebra and be an opposite algebra. Notions of exact andj-positive states of are introduced. It is shown, that any factor state of can be extended to a pure exactj-positive state of . The correspondence generalizes the notion of the purifications map introduced by Powers and Størmer. The factor states ₁ and ₂ are quasi-equivalent if and only if their purifications and are equivalent.     

Coordinates of the quantum plane as q-tensor operators in (\mathfrak{s}\mathfrak{u}(2)*\mathfrak{s}\mathfrak{u}(2))

The relation between the set of transformations of the quantum plane and the quantum universal enveloping algebra U _q (u(2)) is investigated by constructing representations of the factor algebra U _q (u(2))* . The noncommuting coordinates of , on which U _q (2) * U _q (2) acts, are realized as q-spinors with respect to each U _q (u(2)) algebra. The representation matrices of U _q (2) are constructed as polynomials in these spinor components. This construction allows a derivation of the commutation relations of the noncommuting coordinates of directly from properties of U _q (u(2)). The generalization of these results to U _q (u(n)) and is also discussed.     

Regularized,continuum Yang-Mills process and Feynman-Kac functional integral

Giving an ultraviolet regularization and volume cut off we construct a nuclear Riemannian structure on the Hilbert manifold of gauge orbits. This permits us to define a regularized Laplace-Beltrami operator on and an associated global diffusion in governed by . This enables us to define, via a Feynman-Kac integral, a Euclidean, continuum regularized Yang-Mills process corresponding to a suitable regularization (of the kinetic term) of the classical Yang-Mills Lagrangian onT .On leave of absence from Zaragoza University (Spain)Laboratoire associé au CNRS     

Slepton and squark production and decay inep collisions at the LHC

We present a detailed study of and and the subsequent decays of , , and at the LHC . We explore the relevant supersymmetry parameter range. We calculate the cross sections as well as the rates for interesting signatures such as the production of one or two leptons on the lepton side.     

N=2 structures on solvable Lie algebras: Thec=9 classification

Let be a finite-dimensional Lie algebra (not necessarily semisimple). It is known that if is self-dual (that is, if it possesses an invariant metric) then it admits anN=1 (affine) Sugawara construction. Under certain additional hypotheses, thisN=1 structure admits anN=2 extension. If this is the case, is said to possess anN=2 structure. It is also known that anN=2 structure on a self-dual Lie algebra is equivalent to a vector space decomposition , where are isotropic Lie subalgebras. In other words,N=2 structures on in one-to-one correspondence with Manin triples . In this paper we exploit this correspondence to obtain a classification of thec=9N=2 structures on solvable Lie algebras. In the process we also give some simple proofs for a variety of Lie algebras. In the process we also give some simple proofs for a variety of Lie algebraic results concerning self-dual Lie algebras admitting symplectic or Kähler structures.