Study of the three-dimensional Ising model on film geometry with the cluster Monte Carlo method

Topological properties of clusters are used to extract critical parameters. This method is tested for the bulk properties ofd=2 percolation and thed=2, 3 Ising model. For the latter we obtain an accurate value of the critical temperatureJ/k _B T _c=0.221617(18). In the case of thed=3 Ising model with film geometry the critical value of the surface coupling at the special transitions is determined as J_1c/J=1.5004(20) together with the critical exponents ₁ ^m =0.237(5) and=0.461(15).     

O(N) vector model with twisted boundary conditions

Prompted by a recent article of Chakravarty, we reexamine theO(N) vector model with twisted boundary conditions ind dimensions in the various frameworks of the =d–2 expansion, the =4–d expansion, and the large-N expansion. These continuum models describe the physics below the critical temperatureT _c and nearT _c of a latticeO(N) spin model. We determine the effect of the twisting on finite-size scaling functions, for various geometries.On leave from G. Nadjakov Institute of Solid State Physics, 1784 Sofia, Bulgaria.     

Quantum BRST charge for quadratically nonlinear Lie algebras

We consider the construction of a nilpotent BRST charge for extensions of the Virasoro algebra of the form {T _a ,T _b }=f _ab ^c T _c +V _ab ^cd T _c T _d , (classical algebras in terms of Poisson brackets) and [T _a ,T _b ]=h _ab I+f _ab ^c T _c +V _ab ^cd (T _c T _d )(quantum algebras in terms of commutator brackets; normal ordering of the product (T _c T _d ) is understood). In both cases we assume that the set of generators {T _a } splits into a set {H _i } generating an ordinary Lie algebra and remaining generators {S }, such that only theV _ij are nonvanishing. In the classical case a nilpotent BRST charge can always be constructed; for the quantum case we derive a condition which is necessary and sufficient for the existence of a nilpotent BRST charge. Non-trivial examples are the spin-3 algebra with central chargec=100 and theso(N)-extended superconformal algebras with levelS=–2(N–3).     

Anisotropic singlet superconductivity for systems with strongly correlated electrons

The periodic Anderson model extended by pairing interactions amongf- and conduction electrons is investigated in the context of the singlet-like superconductivity. We evaluate the transition temperatureT _c and the ratios of superconducting order parameters atT _c as functions of an effective parameter which describes the correlation off-electrons. The relative stability of thes- andd -superconductivity depends on the values of the Fermi wave vector and on the magnitude of . Due to the absence of on-site pairing forf-electrons, the increase of Coulomb correlations makes thes-like superconductivity more favourable than thed -superconductivity. This behaviour is accompanied by crossover effects: with the increase of Coulomb correlations amongf-electrons the superconductivity is taken over by conduction electrons.Supported by PAN, CPBP 01.12     

Pressure effect onT c and resistivity: Localization in YBa2Cu3O x oxides

We have studied the effect of hydrostatic pressures up to 20 Kbar on the temperature dependence of the resistivity (T) and the effect of quasihydrostatic pressure up to 200 Kbar on the lattice parameters of YBa₂Cu₃O _x for different oxygen concentrations (x=6.95–6.2). Pressure produces a decrease of resistivity in normal state, an increase ofT _c , and a suppression of semiconducting-like resistivity (T) at lowx. The dependence of dT _c (x)/dP onx is nonmonotonic; the record values of dT _c /dP=(1.0±0.1) K/Kbar are observed forx=6.7 and 6.8. The derivative dln/dP atT=293 K differs by the factor 1.8 between superconducting and nonsuperconducting compounds. The compressibility and its pressure derivative alonga, b andc-directions in YBa₂Cu₃O _x have been determined. The most remarkable variation is alongc-direction. A nonmonotonic dependence of dk _c (x)/dP onx has been observed.The results are discussed in the context of localized effects in disordered oxygen-deficient YBa₂Cu₃O _x .     

On the gas-liquid phase transition

A new approach to the problem of the gas-liquid phase transition, based on the Mayer cluster expansion of the partition function, is proposed. It is shown that the necessary and sufficient condition for phase transition to occur is that there exist a temperatureT= T_c > 0 such that forT T _c, all theb _l (except perhaps a finite number of them) are positive, where theb _l, are the cluster integrals (as defined by Mayer) in the thermodynamic limit. Explicit expressions for the isotherms for gas-saturated vapor and liquid phases are given.     

Temperature-dependent electronic structure of gadolinium

We investigate the electronic structure of the ferromagnetic 4f-metal Gadolinium by use of a many-body evaluation of a generalized model of magnetism, the one-particle part of which is derived from an ASW-LSDA bandstructure calculation. A striking temperature-dependence of the conduction band states is traced back to a 4f-(5d, 6s) interband exchange. The conduction electron polarization (0.63 _B atT=0) decreases forTT _c very similar to the 4f-magnetization. A red shift of the lower -band edge of about 0.25 eV appears upon cooling fromT=T _c toT=0. — The quasiparticle band-structure exibits a remarkable non uniform magnetic behaviour at different positions in the Brillouin zone, and in particular for different subbands. Weakly correlated (s-like) dispersions show a Stoner-likeT-dependence of the exchange splitting. On the other hand, stronger correlated (d-like) dispersions split belowT _c into four branches, two for each spin direction. TheirT-dependence mainly concerns the spectral weights of the quasiparticle peaks and not so much the energetic positions. An exchange caused splitting remains even forT<T _c .     

Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order parameter distribution

We consider the rounding and shifting of a firstorder transition in a finited-dimensional hypercubicL ^d geometry,L being the linear dimension of the system, and surface effects are avoided by periodic boundary conditions. We assume that upon lowering the temperature the system discontinuously goes to one ofq ordered states, such as it e.g. happens for the Potts model ind=3 forq3, with the correlation length of order parameter fluctuation staying finite at the transition. We then describe each of theseq ordered phases and the disordered phase forL by a properly weighted Gaussian. From this phenomenological ansatz for the total distribution of the order parameter, all moments of interest are calculated straight-forwardly. In particular, it is shown that forL exceeding a characteristic minimum sizeL _min the forthorder cumulantg _L (T) exhibits a minimum atT _min>T _c, withT _min–T _cL ^–d and the value of the cumulant and the minimum (g(T _min)) behaving asg(T _min)L ^–d. All cumulantsg _L (T) forL approximately intersect at a common crossing pointT _crossL ^–2d, with a universal valueg(T _cross)=1–n/2q, wheren is the order parameter dimensionality. By searching for such a behavior in numerical simulation data, the first order character of a phase transition can be asserted. The usefulness of this approach is shown using data for theq=3,d=3 Potts ferromagnet.     

Dynamics of forest fire under rotational constraint

A rotationally constrained forest fire model is studied on square and triangular lattices of size 400×400. The critical probabilityp _c for onset of fire propagation is determined. The scaling relationsMt ^d _r, R_gt^v andMR _g ^d _f are analysed at fire propagation probabilityp=p _c whereM is the number of burnt trees,R _g the radius of gyration andd _f the fractal dimension of the cluster of burnt trees at timet. Numerical estimates ofd _t, v andd _f have been obtained.     

Valence fluctuations and oxygen dimerization in high-temperature superconductors from X-ray photoemission spectroscopy

The high-temperature superconducting Cu oxides — which are intrinsically Mott insulators — are strongly correlated metals because of valence fluctuations involving Cud ⁹–d ¹⁰ configurations. Temperature-dependent X-ray photoemission spectroscopy of theO 1s and Cu 2p levels in the range 10–300 K provides evidence for O-dimerization, with corresponding increase of the Cud ¹⁰O 2p ⁵ well-screened XPS-final state belowT _c . This supports the suggestion of dynamical mixed-valence and double-exchange antiferromagnetic interaction as an important mechanism for the origin of highT _c superconductivity.     

Is the Cabibbo Angle a Function of the Weinberg Mixing Parameter?

The (u, c) quarks and (d, s) quarks arerequired to have mass matrices of a certainform. To achieve these mass matrices appropriate Lagrangians are assumed. Theu quark is coupled to the standard Higgs scalar _L. Thec quark has a ₅ couplingwith _L and _R, where _R is the Higgs scalar corresponding to theleft-rightmodel. The u quark has no ₅ coupling. Both u,c quarks have a Yukawa couplingwith a Higgs multiplet. Exactly similar Lagrangians are chosen for thed, s qurks.Using these mass matrices, the Cabibbo angle is found to be 13° 11. The ratiom _c/m _s is shown to be approximately 3.1 with the help of the Weinberg mixingparameter. The mixing angles ₂ and ₁ determine the Cabibbo angle. The ratiotan ₂/ tan ₁ is shown to be a function of the Weinberg mixing parameter.     

Theta-point exponent for polymer chain in random media

Using field-theoretic arguments for self-avoiding walks on dilute lattices with site occupation concentrationp, we show that the-point size exponent _p ⁰ of polymer chains remains unchanged for small disorder concentration (p>p _c ). At the percolation thresholdp=p _c , using a Flory-type approximation, we conjecture that _pc ⁰ =5/(d _B +7), whered _B is the percolation backbone dimension. It shows that the upper critical dimensionality for the-point transition atp=p _c shifts to a dimensiond _c >3. We also propose that the-point varies practically linearly withp for 1>pp _c .     

Anisotropic optical properties of single-crystal GdBa2Cu3O7−δ

The optical spectrum of reduced-T _c GdBa₂Cu₃O_7– has been measured for polarizations parallel and perpendicular to theab plane. The sample was an oxygen-deficient single crystal with a large face containing thec axis. The polarized reflectance from this face was measured from 20–300 K in the spectral region from 30–3000 cm^–1, with 300 K data to 30000 cm^–1. Kramers-Kronig analysis was used to determine the spectral dependence of theab and thec components of the dielectric tensor. The optical properties are strongly anisotropic. Theab-plane response resembles that of other reduced-T _c materials whereas thec axis, in contrast, shows only the presence of several phonons. There is a complete absence of charge carrier response alongc aboveand belowT _c. This observation allows us to set an upper limit to the free-carrier spectral weight for transport perpendicular to the CuO₂ planes.Permanent address: Institute of Physics, CSAV, Prague, Czechoslovakia     

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.     

Dimuon production in ultrarelativistic nuclear collisions and QCD phase transitions

Dilepton production rates in nuclear collisions are calculated in order to study their sensitivity to the quark-gluon plasma and to the hadronic phases. This treatment differs from previous work on the subject in two respects: The width of the rho-meson, being exchanged in annihilation, is made temperature dependent, thus taking into account resonance melting as the critical deconfinement temperatureT _d is approached. Secondly, we study in addition to the standard scenario where chiral symmetry restoration and deconfinement occur at the same temperature (T _c =T _d ), an alternative possibility where deconfinement preceeds chiral symmetry restoration (T _d T _c ). Results differ substantially from those obtained assuming a temperature independent rho-meson width, andT _c =T _d .     

Observation of quasi-static spin dynamics in the giant anisotropic ferromagnet PrRu2Si2 by μSR spectroscopy

We report zero field and longitudinal fieldSR measurements on single crystals of the ferromagnet PrRu₂Si₂ (T _c15K). BetweenT=T _c and 250K we observe a quasi-static spin dynamics of the Pr³⁺ ion sub-lattice. BelowT _c, depending on the orientation of the initial muon beam polarisation relative to thec axis of the compound, we find either an oscillating signal or an exponential depolarisation function. These latter data allow us to get information related to the muon in PrRu₂Si₂.     

Fluctuations and lack of self-averaging in the kinetics of domain growth

The fluctuations occurring when an initially disordered system is quenched at timet=0 to a state, where in equilibrium it is ordered, are studied with a scaling theory. Both the mean-sizel(t) ^d of thed-dimensional ordered domains and their fluctuations in size are found to increase with the same power of the time; their relative size fluctuations are independent of the total volumeL ^d of the system. This lack of self-averaging is tested for both the Ising model and the ⁴ model on the square lattice. Both models exhibit the same lawl(t)=(Rt) ^x withx=1/2, although the ⁴ model has soft walls. However, spurious results withx1/2 are obtained if bad pseudorandom numbers are used, and if the numbern of independent runs is too small (n itself should be of the order of 10³). We also predict a critical singularity of the rateR(1–T/T _c) ^v(z–1/x),v being the correlation length exponent,z the dynamic exponent.Also quenches to the critical temperatureT _c itself are considered, and a related lack of self-averaging in equilibrium computer simulations is pointed out for quantities sampled from thermodynamic fluctuation relations.     

Many body contributions to the electronic structure of nickel

The full temperature-dependence of the electronic quasiparticle properties of ferromagnetic Ni is investigated by use of a theoretical model, which takes into account all intraatomic interactions in thed-band complex. After introduction of effective spin operators the model-Hamiltonian consists of a one-particle term, an intraband-interaction of Hubbardtype, and an interband-exchange as in thes-f (ord-f model. The one-particle energies are taken from a realistic bandstructure calculation in order to incorporate approximately all those interactions, which are not directly covered by our model. The model contains two parameters, the intraband couplingU and the interband exchangeJ. ChoosingU=6 eV,J=0.4 eV and applying a Green-function technique we get results in almost quantitative agreement with the experiment:T _c=635 K,m(T=0)=0.56 [ _B , Curie-Weiss behaviour of the static susceptibility, satellite peak with temperature-dependent spinpolarization some 6 eV below the chemical potential , exchange splittings atT=0 of order 0.2–0.35 eV. The full temperature-dependencies of the electronic selfenergy, the one-particle spectral density, the quasiparticle density of states, and the quasiparticle bandstructure for two high symmetry directions are derived and discussed.     

A note on differentiability of the cluster density for independent percolation in high dimensions

The cluster density function of independent percolation in ad-dimensional lattice is considered. For eachn, it is shown that(p) has finitenth leftderivative at critical probabilityp _c ifd is sufficiently large. This result agrees with the Bethe lattice approximation, where thenth one-sided derivative of(p) is bounded atp _c for alln.     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.