Uniform susceptibility of classical antiferromagnets in one and two dimensions in a magnetic field

We simulated the field-dependent magnetization m(H,T) and the uniform susceptibility of classical Heisenberg antiferromagnets in the chain and square-lattice geometry using Monte Carlo methods. The results confirm the singular behavior of at small T,H: and , where D=3 is the number of spin components, J ₀=zJ, and z is the number of nearest neighbors. A good agreement is achieved in a wide range of temperatures T and magnetic fields H with the first-order 1/D expansion results (D.A. Garanin, J. Stat. Phys. 83, 907 (1996)). Received 20 March 2000     

Stretched exponential relaxation on the hypercube and the glass transition

We study random walks on the dilute hypercube using an exact enumeration Master equation technique, which is much more efficient than Monte Carlo methods for this problem. For each dilution p the form of the relaxation of the memory function q(t) can be accurately parametrized by a stretched exponential over several orders of magnitude in q(t). As the critical dilution for percolation is approached, the time constant tends to diverge and the stretching exponent drops towards 1/3. As the same pattern of relaxation is observed in a wide class of glass formers, the fractal like morphology of the giant cluster in the dilute hypercube appears to be a good representation of the coarse grained phase space in these systems. For these glass formers the glass transition may be pictured as a percolation transition in phase space. Received 16 June 2000 and Received in final form 13 October 2000     

Quantum rotors with regular frustration and the quantum Lifshitz point

We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at a multicritical point called a (d,m) quantum Lifshitz point where (d,m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation technique (for finite n). In the spherical limit ()one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m =d though the quantum Lifshitz point exists for all d > 1+m/2, and the upper critical dimensionality is given by d _u = 3 +m/2. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d>m) whereas z=2 in the case of isotropic Lifshitz point (d=m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the quantum Lifshitz point. We have also obtained the exponents in the spherical limit (). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian model by Fisher renormalisation. Received: 23 December 1997 / Received in final form: 6 January 1998 / Accepted: 7 January 1998     

Adhesion-induced lateral phase separation in membranes

Adhesion between membranes is studied using a phenomenological model, where the inter-membrane distance is coupled to the concentration of sticker molecules on the membranes. The model applies to both adhesion of two flexible membranes and to adhesion of one flexible membrane onto a second membrane supported on a solid substrate. We mainly consider the case where the sticker molecules form bridges and adhere directly to both membranes. The calculated mean-field phase diagrams show an upward shift of the transition temperature indicating that the lateral phase separation in the membrane is enhanced due to the coupling effect. Hence the possibility of adhesion-induced lateral phase separation is predicted. For a particular choice of the parameters, the model exhibits a tricritical behavior. We also discuss the non-monotonous shape of the inter-membrane distance occurring when the lateral phase separation takes place. The inter-membrane distance relaxes to the bulk values with two symmetric overshoots. Adhesion mediated by other types of stickers is also considered. Received 12 January 2000 and Received in final form 15 May 2000     

Fully quantum mechanical moment of inertia of a mesoscopic ideal Bose gas

The superfluid fraction of an atomic cloud is defined using the cloud's response to a rotation of the external potential, i.e. the moment of inertia. A fully quantum mechanical calculation of this moment is based on the dispersion of L_z instead of quasi-classical averages. In this paper we derive analytical results for the moment of inertia of a small number of non-interacting Bosons using the canonical ensemble. The required symmetrized averages are obtained via a representation of the partition function by permutation cycles. Our results are useful to discriminate purely quantum statistical effects from interaction effects in studies of superfluidity and phase transitions in finite samples. Received 30 June 2000     

\Lambda, \bar{\Lambda} polarization and spin transfer in lepton deep-inelastic scattering

The flavor and helicity distributions of the and hyperons for both valence and sea quarks are calculated in a perturbative QCD (pQCD) based model. We relate these quark distributions to the fragmentation functions of and , and calculate the z-dependence of the longitudinal spin transfer to and in lepton deep-inelastic scattering (DIS). It is shown that the spin transfer to the is compatible with the first HERMES results at DESY, and further tests are suggested. We also make predictions for the z-dependence of the and longitudinal polarizations in neutrino (antineutrino) DIS processes. We investigate the sea contribution to the fragmentation functions, and we test a possible scenario where the sea quarks in (or the sea antiquarks in ) are negatively polarized, whereas the sea antiquarks in the (or the sea quarks in ) are positively polarized. The asymmetry of the polarized fragmentation functions of the sea quarks and antiquarks to and provides a way to understand the different behavior between the and spin transfers observed in the recent E665 experiment at FNAL. Received: 5 April 2000 / Published online: 26 July 2000     

Sensitivity to initial conditions in the Bak-Sneppen model of biological evolution

We consider biological evolution as described within the Bak and Sneppen 1993 model. We exhibit, at the self-organized critical state, a power-law sensitivity to the initial conditions, calculate the associated exponent, and relate it to the recently introduced nonextensive thermostatistics. The scenario which here emerges without tuning strongly reminds of that of the tuned onset of chaos in say logistic-like one-dimensional maps. We also calculate the dynamical exponent z. Received: 5 November 1997 / Received in final form: 11 November 1997 / Accepted: 19 November 1997     

Local environment and electron correlation effects on the magnetic properties of clusters

The electronic and magnetic properties of clusters are investigated in the framework of the Hubbard model by treating electron correlations effects in a saddle-point slave-boson approximation. The size dependent single-particle spectrum is calculated using a third moment real-space expansion of the local density of states. Results for the magnetic moments, magnetic order, average number of double occupations and hopping renormalizations are given as a function of the local coordination number z, for different representative values of the Coulomb interaction strength U/t and band filling n. Several transitions between paramagnetic, ferromagnetic and antiferromagnetic behaviors are obtained as a function of z. The environment dependence of the magnetic behavior and of the degree of electron delocalization is analyzed. Advantages and limitations of the present approach are discussed. Received: 8 January 1998 / Revised: 22 June 1998 / Accepted: 6 August 1998     

Multi-component structure of nonlinear excitations in systems with length-scale competition

We investigate the properties of nonlinear excitations in different types of soliton carrying systems with long-range dispersive interactions. We show that length-scale competition in such systems, universally results in a multi-component structure of nonlinear excitations which may lead to a new type of multistability: coexistence of different nonlinear excitations at the same value of the spectral parameter (i.e., velocity in the case of anharmonic lattices or frequency in nonlinear Schr?dinger models). Received 31 August 2000 and Received in final form 14 December 2000     

Nucleation-and-growth problem in model lipid membranes undergoing subgel phase transitions is a problem of time scale

In this Rapid Note, we show that the problem of growth of molecular superlattice in a fully hydrated dipalmitoylphosphatidylcholine (DPPC) membrane during the gel-to-subgel phase transformation process is a problem of time scale. There are, in fact, two time scales. The first is an “integrated” or, in some sense, stagnant time scale, that reflects the well-known isotropic growth effect in the d-dimensional space, but assigns the problem to be still in a category of Debye relaxation kinetics. The fraction of old (parent) phase does not suit the Paley-Wiener criterion for relaxation functions, and the time behavior is exclusively due to the geometrical characteristics of the kinetic process. The second (multi-instantaneous) time scale, in turn, is recognised to be a “broken” (fractional time derivative) or memory-feeling (dynamic) scale, which carries some very essential physics of the phenomenon under study, and classifies the problem to be of non-Debye (viz., stretched exponential) nature. It may, in principle, contain all the important effects, like small scale coexistence, presence of collisions between domains, with possible annihilation and creation of domain boundaries, and/or a headgroup packing, hydration against lipid mobility behavior, and finally, a multitude of quasi-crystalline states. It turns out, that within the range of validity of the dynamic scale approximation proposed, the criterion for relaxation functions is very well fulfilled. Received 30 November 1998     

Ground-state properties of the Falicov-Kimball model in one and two dimensions

A new numerical method is used to study the ground-state properties of the spinless Falicov-Kimball model in one and two dimensions. The resultant solutions are used to examine the phase diagram of the model as well as possibilities for valence and metal-insulator transitions. In one dimension a comprehensive phase diagram of the model is presented. On the base of this phase diagram, the complete picture of valence and metal-insulator transitions is discussed. In two dimensions the structure of ground-state configurations is described for intermediate interactions between f and d electrons. In this region the phase separation and metal-insulator transitions are found at low f-electron concentrations. It is shown that valence transitions exhibit a staircase structure. Received 20 October 2000     

Circular-like maps: sensitivity to the initial conditions, multifractality and nonextensivity

Dissipative one-dimensional maps may exhibit special points (e.g., chaos threshold) at which the Lyapunov exponent vanishes. Consistently, the sensitivity to the initial conditions has a power-law time dependence, instead of the usual exponential one. The associated exponent can be identified with 1/(1-q), where q characterizes the nonextensivity of a generalized entropic form currently used to extend standard, Boltzmann-Gibbs statistical mechanics in order to cover a variety of anomalous situations. It has been recently proposed (Lyra and Tsallis, Phys. Rev. Lett. 80, 53 (1998)) for such maps the scaling law , where and are the extreme values appearing in the multifractal function. We generalize herein the usual circular map by considering inflexions of arbitrary power z, and verify that the scaling law holds for a large range of z. Since, for this family of maps, the Hausdorff dimension d_f equals unity for all z in contrast with q which does depend on z, it becomes clear that d_f plays no major role in the sensitivity to the initial conditions. Received 5 February 1999     

Spinodal dewetting of thin liquid films at soft interfaces

We study theoretically the behavior of nanoscopic liquid films L (thickness e) intercalated between a solid S and a rubber R (elastic modulus μ). Thickness modulations involve a healing length , which results from a competition between elastic and disjoining pressure. With van der Waals interactions, , where a is a molecular size and h₀ the rubber capillary length ( , interfacial tension). If the Hamaker constant of the intercalated liquid is negative, the film dewets by amplification of peristaltic fluctuations (“spinodal dewetting”). The typical size of the contacts is predicted to scale like for films of thicknesses . The rise time of the fastest mode, predicted to scale like , should be very sensitive to the film thickness. Received 11 February 2000 and Received in final form 22 May 2000     

Antiferromagnetism and superconductivity in a model with extended pairing interactions

The competition between antiferromagnetism and the d + id superconducting state is studied in a model with near and next near neighbour interactions in the absence of any on-site repulsion. A mean field study shows that it is possible to have simultaneous occurrence of an antiferromagnetic and a singlet d + id superconducting state in this model. In addition, such a coexistence generates a triplet d + id superconducting order parameter with centre of mass momentum Q = (π,π) dynamically having the same orbital symmetry as the singlet superconductor. Inclusion of next nearest neighbour hopping in the band stabilises the d_xy superconducting state away from half filling, the topology of the phase diagram, though, remains similar to the near neighbour model. In view of the very recent observation of a broad region of coexistence of antiferromagnetic and unconventional superconducting states in organic superconductors, the possibility of observation of the triplet state has been outlined. Received 30 November 2000 and Received in final form 27 March 2001     

Decay pathways of small gold clusters

The decay pathway competition between monomer and dimer evaporation of photoexcited cluster ions Au ⁺ _n, n = 2-27, has been investigated by photodissociation of size-selected gold clusters stored in a Penning trap. For n > 6 the two decay pathways are distinguished by their experimental signature in time-resolved measurements of the dissociation. For the smaller clusters, simple fragment spectra were used. As in the case of the other copper-group elements, even-numbered gold cluster ions decay exclusively by monomer evaporation, irrespective of their size. For small odd-size gold clusters, dimer evaporation is a competitive alternative, and the smaller the odd-sized clusters, the more likely they decay by dimer evaporation. In this respect, Au ⁺ ₉ shows an anomalous behavior, as it is less likely to evaporate dimers than its two odd-numbered neighbors, Au ⁺ ₇ and Au ⁺ ₁₁. This nonamer anomaly is typical for copper-group cluster ions M ⁺ ₉ (M = Cu, Ag, Au) and a similar behavior is found in the anionic heptamers M ^- ₇. It is discussed in terms of the well-known electronic shell closing at n _e = 8 atomic valence electrons. Received 2 November 2000     

Effects of solvation on dissociative electron attachment to methyl iodide clusters

Using laser photoelectron attachment to methyl iodide clusters in a differentially-pumped seeded supersonic helium beam and mass spectrometric ion detection, we have measured the rate coefficients for formation of (q = 0-2) ions over the electron energy range 0-100 meV with an effective energy width of about 2.5 meV. Whereas a prominent vibrational Feshbach resonance just below the onset for the C-I stretch vibration ( ) is observed for dissociative attachment to monomers (yielding I^- ions), only weak and broad structure, shifted to lower energies, is detected for formation of ions and essentially no structure is left in the attachment spectrum for . These observations are interpreted by model R-matrix calculations which successfully describe the DA cross-section for the monomer and qualitatively recover the trend observed for cluster ion formation. For the clusters, the effects of increased electron-target long-range interaction and of solvation as well as coupling to soft vibrational modes lead to strong broadening and shifting of the vibrational Feshbach resonance and, ultimately, to its disappearance. Received 29 November 1999 and Received in final form 14 January 2000     

Shear modulus of polydomain, mono-domain and non-mesomorphic side-chain elastomers: Influence of the nematic order

We investigate the behavior of the complex shear modulus of a series of elastomers including mono-domain and poly-domain liquid crystal samples, and a non-mesomorphic sample. We find that the dynamics of the glass transition are strongly modified by the nematic order. This result explains why the truly elastic response of liquid crystal elastomers can only be observed in the isotropic phase at very high temperatures and at very low frequencies. Between the elastic regime and the glassy state, the elastomers have a visco-elastic regime, which is characterized by a Rouse-like behavior for mono-domain and poly-domain samples, and by a Zimm-like behavior for the non-mesomorphic sample. We also show that the mono-domain sample exhibits marked anisotropy of the shear-modulus G ^′. This anisotropy, which is observed for the first time, is a function of frequency and is inverted between low and high frequencies, due to relaxation effects of the orientational order. Received 28 January 2000 and Received in final form 16 October 2000     

Dynamics of selfavoiding tethered membranes. II. Inclusion of hydrodynamic interaction (Zimm model)

The dynamical scaling properties of selfavoiding polymerized membranes with internal dimension D embedded into d dimensions are studied including hydrodynamical interactions. It is shown that the theory is renormalizable to all orders in perturbation theory and that the dynamical scaling exponent z is given by z=d. The crossover to the region, where the membrane is crumpled swollen but the hydrodynamic interaction irrelevant is discussed. The results apply as well to polymers (D=1) as to membranes (D=2). Received: 5 September 1997 / Accepted: 17 November 1997     

Evolution of the electronic structures of NixSiy ordered systems: experimental and theoretical investigations

We study the change of the electronic structures of nickel silicides, Ni₃Si and NiSi₂, as well as nickel and silicon through the evolution of their valence band X-ray photoelectron spectra (v-XPS) both experimentally and theoretically. The experimental spectra are compared to the total and partial densities of states using tight-binding linear muffin-tin orbital method (TB-LMTO) in the atomic sphere approximation (ASA). Good agreement is found between theory and experiment. Received 10 July 2000