The Yang-Lee edge singularity in spherical models

The density of Yang-Lee zeros in the thermodynamic limit is discussed for ferromagnetic spherical models of general dimensionalities and arbitrary range of interaction. In all cases the zeros lie on the imaginary axis in the complex magnetic field planeH=H+iH with a density (H) that exhibits a square root singularity(H) (H-H ₀), with=1/2, as the edge of the gap atH=H ₀(T) is approached forT>T _c. WhenTT _c one hasH ₀(T)(TT _c ) with critical exponent=+.Supported by the National Science Foundation in part through the Materials Science Center at Cornell University.     

Pseudogap in the electronic density of states of superconducting glasses

Two loop order results for the electronic density of states (DOS) of both Ising- and XY-type superconducting glass phases are presented. Maximal depression of the DOS by critical fluctuation corrections to its finite mean field value is found to occur at the Fermi energyE _F . The theory is renormalizable and exponentiation of the loop expansion yields (E _F)=0 for the DOS in two dimensions and for arbitrarily small disorder. It is also concluded that the DOS assumes nonzero values, when either |E–E _F|, or magnetic field H, or temperature T become nonzero. A pseudogap (atT=0,H=0) or a smeared gap (forH0 orT0) is thus obtained with a DOS-minimum at the Fermi level. A rough estimate of the effective width is given. In three dimensions, the DOS atE _F vanishes like (n _c ^I –n)^1/2 for the Ising-type glass and like (n _c ^XY –n)¹ for the XY-type glass as the impurity concentrationn exceeds characteristic values. At second loop order, the calculation contains a nontrivial indication of a lower critical dimension two.     

Critical thermodynamics of dysprosium ethyl sulphate, a pure dipolar Ising ferromagnet

Using a SQUID magnetometer the magnetization of the Ising ferromagnet dysprosium ethyl sulphate has been measured in the temperature range 0.015–3K and in external fields 0.004–30 Oe. The results atT0.4 K (precritical regime) confirm the pure dipolar nature of the magnetic interactions. Particular interest has been paid to the immediate neighbourhood of the critical pointT _c =118.17 mK andH=0 where the zero-field susceptibility(T) aboveT _c , the spontaneous magnetizationM _s (T), and the magnetization atT _c ,M _c (H), can be described by mean field laws modified by logarithmic singularities. The critical amplitudes, B, andD of, M _s andM _c , respectively, satisfy the relation (2/3B ²)^1/3=D. All these results agree with predictions of (i) the Larkin-Khmel'nitskii theory and (ii) exact solutions of the renormalization group equations for 3-dimensional dipolar Ising ferromagnets.     

Dynamics of the generalized Glauber-Ising chain in a magnetic field

A one-dimensional kinetic Ising model with nearest neighbor interactionJ and magnetic fieldH 0 is treated in both linear and nonlinear response, using the most general single spin-flip transition probabilities that depend on nearest neighbor states only. The dynamics is reformulated in terms of kinetic equations for the concentration n_l ⁺(t) [@#@ n_l(t) of clusters containingl up- [or down-] spins, which is exact in the homogeneous case. The initial relaxation time ^* of the magnetization is obtained rigorously for arbitraryJ, H, and temperatureT. The relaxation function is found by numerical integration forJ/T < 2. It is shown that coagulation of minus-clusters becomes negligible for bothJ/T andH/T large, and the resulting set of equations is solved exactly in terms of an eigenvalue problem. A perturbation theory is developed to take into account the neglected coagulation terms. The relaxation function is found to be non-Lorentzian in general, in contrast to the Glauber results atH = 0, which are recovered as a special case. In addition, nonlinear and linear relaxation functions differ forH 0. Consequences for the application to biopolymers are briefly mentioned.Supported in part by the Deutsche Forschungsgemeinschaft (SFB 130).     

Temperature dependence of viscosity near the glass transition

Real glass transitions, where activated processes are included, are analysed near Whitney fold and cusp singularities. In particular the temperature dependence of the viscosity is studied. For sufficiently strongly coupled systems there is close to a fold singularity located atT=T _c , a crossover from an algebraic divergence (T–T _c )^– forT>T _c , to an Arrhenius dependence exp(E/k _B T) forT<T _c . If a parameter vector specifying the system also passes close to a cusp singularity, atT ₀<T _c , there may be a temperature region where the viscosity also shows Fogel-Fulcher like dependence. The results for the viscosity are intimately connected with the dynamics for the so-called -relaxation process, where relaxation occurs via a fractal time process in the delevant time region.     

Dynamics of vector spin glasses: The Gabay-Toulouse line

The dynamics of ann-component vector spin glass with infinite range interactions are investigated near and above the Gabay-Toulouse (GT) line. The local transverse susceptibility _T for 0 varies along the whole GT lineT _c1 (H) as ^v , with a field and temperature independent critical exponentv=1/2. The longitudinal susceptibility _L () remains analytic for all (T, H)T _c1 (H), except for a cross-over fromv=1 tov=1/2 forH0 at the freezing temperatureT=T _f . The dynamic susceptibilities _T () and _L () are already coupled above the GT line via self-energy terms. BelowT _c1 (H), this coupling is strongly enhanced by other mechanisms.     

Diffusion in a periodic potential with a local perturbation

We consider the diffusion of a particle at X_t in a drift field derived from a smooth potential of the formV+B, whereV is periodic andB is a bump of compact support. With no bump,B=0, the mean squared displacementE(t) E |X _t – X₀|² =D(V)t +C +O(e ^–t ),>0, in any dimension. WhenB0, we establish in one dimension the asymptotic expansion , 0, ast. Our analysis relies on the Nash estimates developed in previous work for the transition density of the process and their consequences for the analytic structure,of the Laplace transform ofE(t).     

Nonequilibrium phase transition in stochastic lattice gases: Simulation of a three-dimensional system

We report results of computer simulations of a three-dimensional lattice gas of interacting particles subject to a uniform external fieldE. The dynamics of the system is given by hoppings of particles to nearby empty sites with rates biased for jumps in the direction ofE. As for the two-dimensional system we find that here too there exists a critical temperature,T _c (E) such that forT < T _c (E) the systems orders in a very anisotropic phase with striplike typical configurations parallel to the field.T _c (E) increases withE but substantially less strongly than in two dimensions. There is a break in the slope of the saturation current atT _c (E). Our data are consistent with the critical exponent being mean field.     

Internal Lifschitz singularities of disordered finite-difference Schrödinger operators

The integrated density of states has C-like singularities, ln|k(E)–k(E _c )|=–|E–E _c |^–v/2 _c (E), with _c >0, a milder function at the edges of the spectral gaps which appear when the distribution function of the potentiald has a sufficiently large gap. The behaviour of _c nearE _c is determined by the local continuity properties ofd near the relevant edge: _c (E)=O(1) ifd has an atom and =O(ln|E–E _c |) if is (absolutely) continuous and power bounded.     

Reversible dynamics and the macroscopic rate law for a solvable Kolmogorov system: The three bakers' reaction

We investigate a piecewise linear (area-preserving) mapT describing two coupled baker transformations on two squares, with coupling parameter 0c1. The resulting dynamical system is Kolmogorov for anyc0. For rational values ofc, we construct a generating partition on whichT induces a Markov chain. This Markov structure is used to discuss the decay of correlation functions: exponential decay is found for a class of functions related to the partition. Explicit results are given forc=2^–n. The macroscopic analog of our model is a leaking process between two (badly) stirred containers: according to the Markov analysis, the corresponding progress variable decays exponentially, but the rate coefficients characterizing this decay are not those determined from the one-way flux across the cell boundary. The validity of the macroscopic rate law is discussed.     

On the Fokker-Planck equation with time-dependent drift and diffusion coefficients and its exponential solutions

The static critical behavior of a mixed hydrogen-bonded ferro-antiferroelectric system is investigated with use of a pseudo-spin Ising model in a transverse field, which describes the tunneling of protons. Assuming an infinite-ranged random interbond coupling, then0 replica method is applied to evaluate the averaged free energy, from which the replica-symmetric solution of the Sherrington-Kirkpatrick type is obtained. It is shown that a proton pseudo-spin glass (PG) phase exists below a freezing temperatureT _f , whereT _f and the order parameters for the PG and ferroelectric phase are parametrized by the tunneling frequency . For _c, where _c = and is the random distribution width, no ordering is possible even forT0. Numerical solutions for the PG order parameter and the dielectric susceptibility atT0 are obtained, and the phase diagram for a simple model of a mixed system atT0 is presented.Dedicated to Prof. Dr. H.E. Müser on the occasion of his 60th birthday     

A theoretical prediction for exclusive decaysB→K(K*)η c

The decay rates for the exclusiveB decaysBK _c andBK* _c are calculated in the context of the heavy quark effective theory. We obtain(BK _c )/ (BK)=1.6±0.2 and(BK* _c )/ (K*)=0.39±0.04. These results lead to estimates BR(BK _c )=(0.11±0.02)% and BR(BK* _c )=(0.05±0.01)% if we use the central current experimental values forB(K, K ^*) branching ratios.     

The homogeneity of the ball inR 3 and special relativity

Einstein's velocity addition formula ofspecial relativity (SR) defines a transformation _v of the ballB _c of radiusc inR ³, representing all possible velocities in an inertial systemK, onto identical ballB _c , which represents the velocities in another systemK, moving with velocity v relative toK. Since _v maps the zero velocity ofB _c into arbitrary vector v ofB _c ,B _c is homogeneous under all possible _v.A similar homogeneity of the unit ballB inL(G, H) under a set of maps _a, a B, arises also in theLine Transmission Theory (TLT) for a lossless line. HereL(G, H) is the space of all linear operators between Hilbert spacesG,H, representing the signals on the line in the two directions. The explicit form of _a is obtained naturally in TLT.     

The Role of the Hall Field in the Transverse Magnetotransport

The direct measurements show that the Hall field makes no contribution to the electric-field electron heating. The volt-ampere characteristics of n-InSb are measured at T = 4.2 K and the quantizing magnetic field up to 7.4 T for E _y = 0 and E _y 0. A significant effect of the Hall-contact shorting on the magnetoresistance oscillation curve is revealed.     

a-b plane anisotropy of single-domain crystals of Bi2Sr2CaCu2O8

The polarized reflectance of thea-b plane of single-domain Bi₂Sr₂CaCu₂O₈ crystals is anisotropic above and belowT _c . The normal-state infrared conductivity is higher forEa whereas the high-frequency conductivity is higher alongb, particularly for transitions associated with the Bi–O layers. BelowT _c there is a definite anisotropy to the far-infrared absorption, with a finite absorption forEb down to 20 meV. This anisotropy of thea-b plane could be due either to anisotropy of the superconducting gap or to anisotropy of the midinfrared component to the conductivity.     

Nonlinear relaxation at first-order phase transitions: A Ginzburg-Landau theory including fluctuations

Kinetics of phase transitions are investigated in systems with nonconserved one-component order parameter (i.e., generalized time-dependent Ginzburg-Landau models ind dimensions). The correct static critical behavior as well as fluctuation effects on the kinetics are incorporated by a suitable adaptation of the theory on spinodal decomposition by Langer, Baron and Miller. Both the case of quenches from temperaturesT above to below the critical pointT _c and the case of magnetic field changesH from positive to negative values are treated, and both time-dependent order parameter m() and structure factorS(q, ) are obtained numerically ford=2, 3. In the case of quenches atH=0, we find that m()0 andS(q, ) —S(q, ) exp(– ^1/2/7.2) , withS(q, )q ^–2. In the case of field changes we find that forH not exceeding some critical valueH ^* the system is trapped in a metastable state with infinite lifetime. In contrast to the meanfield-spinodal, the susceptibility does not seem to diverge atH ^*. These results are compared with other treatments, in particular the Monte Carlo simulations of kinetic Ising models by Binder and Müller-Krumbhaar. While our theory describes some properties of the metastable states reasonably,H ^* distinctly exceeds the observed limit of metastability. We argue that the present theory does not take into account nucleation fluctuations, and also fails to describe correctly the domain growth in the late stages of the relaxation. Contrary to Langer et al. we suggest that universality holds for nonlinear relaxation and spinodal decomposition nearT _c .Supported in part by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 130     

Masses of colored vector mesons

Mass formulas for colored vector mesons are derived under the assumption of one common mixing angle forSU(3), independent of the color quantum numbers, and correspondingly one common mixing angle () forSU(3). This a priori plausible assumption turns out to have strong implications and thus might be too restrictive. We allow for a non-trivial spatial overlap integral between color-singlet and color-octet states. Various cases are treated and physical possibilities are identified. The best agreement is obtained for = 0. There are two models of this type with and without a part of the symmetry breaking Hamiltonian density transforming as (Y, Y) underSU(3)SU(3). Models with 0 are also possible. They cannot have a (Y, Y) and predict 3.34 GeV as the mass of the (3.7). This error of 10% may however be used to reject this possibility. Masses of colored vector mesons are predicted in the various models. If a (Y, Y) is present, ideal mixing inSU (3) is implied by the general formalism of the model.     

Regular Self-Consistent Geometries with Infinite Quantum Backreaction in 2D Dilaton Gravity and Black Hole Thermodynamics: Unfamiliar Features of Familiar Models

We analyze the rather unusual properties of some exact solutions in 2D dilaton gravity for which infinite quantum stresses on the Killing horizon can be compatible with regularity of the geometry. In particular, the Boulware state can support a regular horizon. We show that such solutions are contained in some well-known exactly solvable models (for example, RST). Formally, they appear to account for an additional coefficient B in the solutions (for the same Lagrangian which contains also traditional solutions) that gives rise to the deviation of temperature T from its Hawking value T _H . The Lorentzian geometry, which is a self-consistent solution of the semiclassical field equations, in such models, is smooth even at B0 and there is no need to put B=0 (T=T _H ) to smooth it out. We show how the presence of B0 affects the structure of spacetime. In contrast to usual black holes, full fledged thermodynamic interpretation, including definite value of entropy, can be ascribed (for a rather wide class of models) to extremal horizons, not to nonextreme ones. We find also new exact solutions for usual black holes (with T=T _H ). The properties under discussion arise in the weak-coupling regime of the effective constant of dilaton-gravity interaction. Extension of features, traced in 2D models, to 4D dilaton gravity leads, for some special models, to exceptional nonextreme black holes having no own thermal properties.     

Analyticity of correlation functions for the two-dimensional Ising model

Analyticity of correlation functions for the two-dimensional Ising model as a function of the inverse temperature except for the singularity at the critical temperature is proved. A crucial step is the establishment of the correspondence between extremal equilibrium states of the model and pure ground states of a one-dimensional spin system below the critical temperatureT _c . An exact decay rate of the clustering property along axes is also determined for allTT _c .