Self-consistent perturbation theory for dynamics of valence fluctuations

Dynamical as well as equilibrium properties of model Ce systems are investigated in both the intermediate-valence and nearly integral-valence (Kondo) regimes at finite temperatures. With self-consistent account of hybridization effects between the conduction bands and the highly correlated 4f states, the 4f-electron density of states _4f () and the dynamical magnetic susceptibility () are derived. Equilibrium properties such as the static magnetic susceptibility and the averaged 4f-electron number are also computed within the same approximation scheme that neglects intersite interactions between different Ce ions. In the intermediate-valence regime the calculated line-shape of Im ()/ is close to the Lorentzian at high temperatures, but at low temperatures there appears an inelastic peak. In the Kondo regime it is shown that a sharp peak in _4f () develops at the Fermi level as the temperature decreases. The line-shape of Im ()/ is shown to be close to the Lorentzian at all temperatures. The half-width is considerably enhanced over the Korringa value expected for the local-moment system. The temperature dependence of the half-width agrees qualitatively with experimental results in Kondo compounds such as CeB₆, CeCu₂Si₂ and CeAl₃.     

Multiatom interactions,order and stability in binary transition metal alloys

Interface delocalization or depinning transitions such as wetting or surface induced disorder are considered. At these transitions, the correlation length for transverse correlations parallel to the surface diverges. These correlations are studied in the framework of Landau theory. It is shown the t^–1/2 at all types of transitions for systems with short-range forces wheret measures the distance from bulk coexistence.     

Asymptotically abelian systems

We study pairs { , } for which is aC*-algebra and is a homomorphism of a locally compact, non-compact groupG into the group of *-automorphisms of . We examine, especially, those systems { , } which are (weakly) asymptotically abelian with respect to their invariant states (i.e. |A _g (B) — _g (B)A 0 asg for those states such that ( _g (A)) = (A) for allg inG andA in ). For concrete systems (those with -acting on a Hilbert space andg _g implemented by a unitary representationg U _g on this space) we prove, among other results, that the operators commuting with and {U _g } form a commuting family when there is a vector cyclic under and invariant under {U _g }. We characterize the extremal invariant states, in this case, in terms of weak clustering properties and also in terms of factor and irreducibility properties of { ,U _g }. Specializing to amenable groups, we describe operator means arising from invariant group means; and we study systems which are asymptotically abelian in mean. Our interest in these structures resides in their appearance in the infinite system approach to quantum statistical mechanics.     

On the chiral hubbard model and the chiral Kondo lattice model

The integrability of the one-dimensional chiral Hubbard model is discussed in the limit of strong interaction,U=. The system is shown to be integrable in the sense of the existence of an infinite number of constants of motion. The system is related to a chiral Kondo lattice model at strong interactionJ=+.     

A complementary thermodynamic limit for classical Coulomb matter

The canonical equilibrium measure of classical two-component Coulomb matter with regularized interactions is analyzed in a finite volume. It is shown that, in the mean-field regime, the one-particle density is inhomogeneous on a new characteristic length scale _inh. For a system ofN positive andN negative particles, _inh and the characteristic length scale of correlations _corr (=Debye screening length) are related via _inh=(2N)^1/2 _corr. The major conceptual conclusion that is drawn from this is that one needs two nontrivial complementary thermodynamic limits to define the equilibrium thermodynamics of two-component Coulomb systems. One of them is the standard thermodynamic limit (infinite volume), where one takesN, _corr fixed. Its complementary limit is characterized byN, _inh fixed, and is a finite-volume inhomogeneous mean-field limit. The most prominent new feature in the mean-field thermodynamic limit, which is absent in the standard thermodynamic limit, is an anomalous first-order phase transition where the Coulomb system explodes or implodes, respectively. The phase transition is connected with the existence of a metastable plasma phase far below the ionization temperature.     

Anisotropy of the low temperature resistivity of hexagonal single crystalline spin glass systems

The impurity contribution to the resistivity in zero field (T) of dilute hexagonal single crystals of ZnMn, CdMn and MgMn has been studied in the mK range on samples cut parallel () and perpendicular () to thec-axis, using a SQUID technique for the measurements. Typical spin glass behavior is found in (T) as well as (T) for all alloys, with Kondo like logarithmic increases at higher temperatures and maxima atT _m at lower temperatures, indicating the influence of impurity interactions. The differences in the corresponding isotropic resistivity _poly(T) between the three systems can qualitatively be understood within the framework of a theoretical model by Larsen, describing (T) as a function of universal quantitiesT/T _K and _RKKY/T _K , where _RKKY is the RKKY-interaction strength andT _K the Kondo temperature. With respect to the two lattice directions studied, the behavior of (T and (T is anisotropic in the Kondo regime as well as in the range where ordering becomes important. While the anisotropy in the Kondo slope can be understood by an anisotropic unitarity limit, the understanding of the anisotropy in region where impurity interactions are important remains problematic.Dedicated to Prof. Dr. S. Methfessel on the occasion of his 60th birthday     

Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m ²+|b/4|m ⁴–mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h _J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h _J,h) is related to intrinsically large FPT fluctuations ( ²–²)/ ² O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.     

The velocity autocorrelation function of a finite model system

We investigate in detail the dependence of the velocity autocorrelation function of a one-dimensional system of hard, point particles with a simple velocity distribution function (all particles have velocities ±c) on the size of the system. In the thermodynamic limit, when both the number of particlesN and the length of the boxL approach infinity andN/L , the velocity autocorrelation function(t) is given simply by c² exp(–2ct@#@). For a finite system, the function _N(t) is periodic with period 2L/c. We also show that for more general velocity distribution functions (particles can have velocities ±c_i,i = 1,...), _N(t) is an almost periodic function oft. These examples illustrate the role of the thermodynamic limit in nonequilibrium phenomena: We must keept fixed while letting the size of the system become infinite to obtain an auto-correlation function, such as(t), which decays for all times and can be integrated to obtain transport coefficients. For any finite system, our _N (t) will be very close to(t) as long ast is small compared to the effective size of the system, which is 2L/c for the first model.Supported in part by the AFOSR under Contract No. F44620-71-C-0013.     

Discontinuity of the magnetization in one-dimensional 1/¦x−y¦2 Ising and Potts models

Results from percolation theory are used to study phase transitions in one-dimensional Ising andq-state Potts models with couplings of the asymptotic formJ _x,y const/¦x–y¦². For translation-invariant systems with well-defined lim _x x ² J _x =J ⁺ (possibly 0 or ) we establish: (1) There is no long-range order at inverse temperatures withJ ⁺1. (2) IfJ ⁺>q, then by sufficiently increasingJ ₁ the spontaneous magnetizationM is made positive. (3) In models with 0<J ⁺< the magnetization is discontinuous at the transition point (as originally predicted by Thouless), and obeysM( _c )1/( _c J ⁺)^1/2. (4) For Ising (q=2) models withJ ⁺<, it is noted that the correlation function decays as xy()c()/|x–y|² whenever< _c . Points 1–3 are deduced from previous percolation results by utilizing the Fortuin-Kasteleyn representation, which also yields other results of independent interest relating Potts models with different values ofq.     

Geometric localization of the threshold in two-dimensional Ising ±J spin glasses forT=0

Following an approach of Toulouse, ground states in random 2D Ising ±J spin glasses (without external magnetic field), on square lattices, and with concentrations 0p0.5 of antiferromagnetic bonds are studied by means of minimal matchings of frustrated plaquettes. Lete(p) be the ground-state energy per spin in the thermodynamic limit. Then the well-known equatione(p)=–2+(p)f(p) holds, wheref(p) is the concentration of frustrated plaquettes and(p) is the average connection length between paired frustrated plaquettes in minimal matchings. Introducing (p) as the probability that a frustrated plaquette is matched to another frustrated plaquette by a connection of length (in a minimal matching), the average length(p) can be rewritten asgl(p)=(p). The study of(p) and its components (p) leads to an intervalp ^*pp ₂ (p ^*0.121±0.008,p ₂0.161±0.008) where the threshold between ferromagnet and paramagnet forT=0 lies. Analyzing a similar so-called adjoined average lengthl(p) admits further insight.     

On a limiting procedure for obtaining physical states for an infinite Fermi system

We propose a limiting procedure for obtaining physical states for an infinite non-relativistic Fermi system. We take the thermodynamic limit of vector states in the Fock representation of the C.A.R. algebra, representing a condensate state of atoms each of which is formed by 4 fermions. In a simplified example considered in detail, the limit state has a simple decomposition into the product of two B.C.S. states. IfB ⁺ is the operator creating the atom from the vacuum |_0F , it is proved that the states obtained by taking the thermodynamic limit of the vector states corresponding to (B ⁺) ⁿ |_0F and respectively, coincide on the gauge-invariant elements of the algebra for a suitable value ofz.Partially supported by C.N.R.     

Change in primary extinction of X-rays in solid solution of NaCl-CdCl2

The Suzuki model of regions with a hyperstructure was verified, the dependence of their size on the cooling rate was found and it was determined that they disappear at temperatures between 250° and 300°C according to their composition. Up to 1000 Å their structure is coherent with a matrix lattice and their formation is not accompanied by a decrease in the primary extinction. Regions above 1000 Å are partially incoherent and their formation and disappearance are apparent by a change in the primary extinction.

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NaCl-CdCl₂

, , , 250°–300°C . , 1000 Å, . , 1000 Å, .

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The author would like to thank I. Kunzlová, and M. Lébl for preparing the crystals of NaCl-CdCl₂ solid solution and Dr. Trnka for determining the cadmium Concentration in them.     

Fluids with highly directional attractive forces. I. Statistical thermodynamics

A new formulation of statistical thermodynamics is derived for classical fluids of molecules that tend to associate into dimers and possibly highers-mers due to highly directional attraction. A breakup of the pair potential into repulsive and highly directionally attractive parts is introduced into the expansion of the logarithm of the grand partition function in fugacity graphs. The bonding by the directional attraction is used to classify the graphs and to introduce a topological reduction which results in the replacement of the fugacity by two variables: singlet density and monomer density ₀. Results for the thermodynamic functions as functionals of and ₀ are given in the form of graph sums. Pair correlations are analyzed in terms of a new matrix analog of the direct correlation function. It is shown that the low-density limit is treated exactly, while major difficulties arise when the Mayer expansion, which employs onlyp, is used. The intricate resummations required for the Mayer expansion are illustrated for the case where dimers are the only association products.Supported by the NSF under Grant Nos. CHE-81-14968 and CHE-82-11236 and by the U.S. Air Force under Grant No. AFOSR 82-0016A.     

Generalized Bethe ansatz solution of a one-dimensional asymmetric exclusion process on a ring with blockage

We present a model for a one-dimensional anisotropic exclusion process describing particles moving deterministically on a ring of lengthL with a single defect, across which they move with probability 0 p 1. This model is equivalent to a two-dimensional, six-vertex model in an extreme anisotropic limit with a defect line interpolating between open and periodic boundary conditions. We solve this model with a Bethe ansatz generalized to this kind of boundary condition. We discuss in detail the steady state and derive exact expressions for the currentj, the density profilen(x), and the two-point density correlation function. In the thermodynamic limitL the phase diagram shows three phases, a low-density phase, a coexistence phase, and a high-density phase related to the low-density phase by a particle-hole symmetry. In the low-density phase the density profile decays exponentially with the distance from the boundary to its bulk value on a length scale . On the phase transition line diverges and the currentj approaches its critical valuej _c = p as a power law,j _c – j ^–1/2. In the coexistence phase the width of the interface between the high-density region and the low-density region is proportional toL ^1/2 if the density f 1/2 and=0 independent ofL if = 1/2. The (connected) two-point correlation function turns out to be of a scaling form with a space-dependent amplitude n(x₁, x₂) =A(x₂)A ^Ke^–r/ withr = x ₂ –x ₁ and a critical exponent = 0.     

Bethe-Ansatz solution of the ground-state of theSU (2j+1) Kondo (Coqblin-Schrieffer) model: Magnetization,magnetoresistance and universality

The magnetization, the magnetoresistance and the populations of the spin components of the Coqblin-Schrieffer model forj5/2 are calculated from the Kondo limit of a mixed-valence model discussed previously. The results forj=1/2 andj=1 agree with those given in the literature. Forj3/2 only an approximate solution of the integral equations is given, which interpolates between the exact low and high-field results. The universality is discussed and the exact Wilson-numbers are obtained. The Kondo limit of the mixed-valent model is shown to be equivalent to the Coqblin-Schrieffer model by using the Bethe-ansatz equations.     

The Heisenberg ferromagnet as a quantum field theory

We consider a lattice of spin 1/2 ions, described by the discrete form of the current commutation relationsJ _i J _(i) =1/2, [J _i ,J _i ]=i _ij J _i where =1, 2, 3 andi label the lattice sites. The algebra is realized as the Clifford algebra over a Hilbert space. The equations of motion are specified by a formal Hamiltonian of the Heisenberg form: , wheref _ij 0 and only a finite numberQ of ions are linked to any given lattice site. We prove that the Hamiltonian is non-negative in a representation of , and has a ground state exhibiting ferromagnetism. The time displacement group acts continuously on , inducing automorphisms. is asymptotically abelian with respect to the space translations of the lattice.The model is an example of an algebraic quantum field theory and possesses a broken symmetry, the rotation group 0(3). The consequent Goldstone theorem is proved, namely, there is no energy gap in the spectrum ofH.     

Phase Transitions in a Driven Lattice Gas with Anisotropic Interactions

The Ising lattice gas, with its well known equilibrium properties, displays a number of surprising phenomena when driven into nonequilibrium steady states. We study such a model with anisotropic interparticle interactions (J _||J ), using both Monte Carlo simulations and high temperature series techniques. Under saturation drive, the shift in the transition temperature can be both positive and negative, depending on the ratio J _||/J ! For finite drives, both first- and second-order transitions are observed. Some aspects of the phase diagram can be predicted by investigating the two-point correlation function at the first nontrivial order of a high-temperature series expansion.     

The magnetic behavior of CeB6: Comparison between elastic and inelastic neutron scattering,initial susceptibility and high-field magnetization

We report measurements of the elastic and inelastic neutron scattering, initial susceptibility and high-field magnetization on thoroughly prepared poly- and single crystalline samples of CeB₆. Part of these experiments have been performed at temperatures down to 60 mK and magnetic fields up to 70 kØe. Our neutron-diffraction data provide the first proof that CeB₆ is an antiferromagnet belowT _N2K as has been suggested by previous bulk experiments. The reduced value of the low-temperature magnetic moment both below and aboveT _N points to the existence of a Kondo effect of the ₇ crystal-field (CF) ground state of Ce³⁺. From the low-temperature width of the quasielastic neutron line, the Kondo temperature is inferred to beT _K3 K. The thermal variation of the initial susceptibility (forT>20K) is semiquantitatively explained invoking, besides the Kondo effect, a ₇- ₈ CF splitting of 70 K and magnetic interactions, which are about 10 times stronger between ₈ states than those between ₇ states. This large ₈- ₈ exchange interaction is also assumed to account for the most striking result of this work, i.e. the lack of any CF-transition peak up to 44 meV in our inelastic neutron-scattering spectra.     

Elimination of variables in simple laser equations

The usual way of obtaining rate equations (RE) and a single equation for the field amplitude (EFA) from the semiclassical laser equations (Lorenz-Haken model) is reexamined by undertaking a systematic elimination procedure developed in synergetics. The RE and EFA are justified in the case 1 (, ) and case 2 (, ), respectively. We show that, because the eliminated variable happens to contain a considerable contribution from an unstable mode, the usual elimination technique in the case 3 (, ) leads to an inconsistency. As important by-products we obtain the RE and EFA for arbitrary cavity relaxation constant (). Some remarks are given on the direct elimination technique in the non-diagonal representation in the study of instabilities.     

Metastates in Disordered Mean-Field Models II: The Superstates

We continue to investigate the size dependence of disordered mean-field models with finite local spin space in more detail, illustrating the concept of superstates as recently proposed by Bovier and Gayrard. We discuss various notions of convergence for the behavior of the paths (t_[tN]()) _{t(0, 1]} in the thermodynamic limit N. Here _n () is the Gibbs measure in the finite volume {1,..., n} and is the disorder variable. In particular we prove refined convergence statements in our concrete examples, the Hopfield model with finitely many patterns (having continuous paths) and the Curie–Weiss random-field Ising model (having singular paths).