Effects of random biquadratic couplings in a spin-1 spin-glass model

A spin-1 model, appropriated to study the competition between bilinear (J _ij S _i S _j ) and biquadratic (K _ij S _i ² S _j ²) random interactions, both of them with zero mean, is investigated. The interactions are infinite-ranged and the replica method is employed. Within the replica-symmetric assumption, the system presents two phases, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic couplings between the spins. Received 18 May 1999 and Received in final form 20 October 1999     

High-temperature series analysis of the p-state Potts glass model on d-dimensional hypercubic lattices

We analyze recently extended high-temperature series expansions for the “Edwards-Anderson” spin-glass susceptibility of the p-state Potts glass model on d-dimensional hypercubic lattices for the case of a symmetric bimodal distribution of ferro- and antiferromagnetic nearest-neighbor couplings . In these star-graph expansions up to order 22 in the inverse temperature , the number of Potts states p and the dimension d are kept as free parameters which can take any value. By applying several series analysis techniques to the new series expansions, this enabled us to determine the critical coupling K_c and the critical exponent of the spin-glass susceptibility in a large region of the two-dimensional (p,d)-parameter space. We discuss the thus obtained information with emphasis on the lower and upper critical dimensions of the model and present a careful comparison with previous estimates for special values of p and d. Received: 25 May 1998 / Revised and Accepted: 11 August 1998     

Model glasses coupled to two different heat baths

In a p-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change with time. The spins are coupled to a heat bath with temperature T, while the coupling constants are coupled to a bath having temperature T_J. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, n=T/T _J . For p>2 there occur at low temperatures two different glassy phases, depending on the value of n. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is an essentially non-equilibrium effect. The dynamical phase transition exists only for n<1. For p=2 correlation of the disorder (leading to a non-zero n) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived. Received 12 July 1999 and Received in final form 8 December 1999     

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     

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     

Non-linear response and electron-electron interactions in mesoscopic metal rings

A time-dependent electric field gives rise to a stationary non-equilibrium current I ⁽²⁾ around a mesoscopic metal ring threaded by a magnetic flux. We show that this current, which is proportional to the intensity of the field, is closely related to the exchange part of the interaction contribution to the equilibrium persistent current, and that the corresponding non-linear conductivity directly measures the weak localization correction to the polarization. We explicitly calculate the disorder average of I ⁽²⁾ in the diffusive regime as function of the frequency of the electric field and the static flux piercing the ring, and suggest an experiment to test our theory. Received: 5 September 1997 / Accepted: 4 November 1997     

Intrusion of fluids into nanogrooves

We study the shape of gas-liquid interfaces forming inside rectangular nanogrooves (i.e., slit-pores capped on one end). On account of purely repulsive fluid-substrate interactions the confining walls are dry (i.e., wet by vapor) and a liquid-vapor interface intrudes into the nanogrooves to a distance determined by the pressure (i.e., chemical potential). By means of Monte Carlo simulations in the grand-canonical ensemble (GCEMC) we obtain the density ρ(z) along the midline (x = 0 of the nanogroove for various geometries (i.e., depths D and widths L of the nanogroove. We analyze the density profiles with the aid of an analytic expression which we obtain through a transfer-matrix treatment of a one-dimensional effective interface Hamiltonian. Besides geometrical parameters such as D and L , the resulting analytic expression depends on temperature T , densities of coexisting gas and liquid phases in the bulk ρ^g,l _x and the interfacial tension γ . The latter three quantities are determined in independent molecular dynamics simulations of planar gas-liquid interfaces. Our results indicate that the analytic formula provides an excellent representation of ρ(z) as long as L is sufficiently small. At larger L the meniscus of the intruding liquid flattens. Under these conditions the transfer-matrix analysis is no longer adequate and the agreement between GCEMC data and the analytic treatment is less satisfactory.     

Rheological behaviour and shear thickening exhibited by aqueous CTAB micellar solutions

In this experimental work we carefully investigate the rheological behaviour and in particular the shear thickening exhibited by aqueous micellar solutions of CTAB with NaSal as added counterion. We are particularly interested in the evolution of the critical shear rate (at which shear thickening occurs) versus C _D , the surfactant concentration. We show that , at fixed salt concentration C _S , increases with C _D following a power law evolution with a positive exponent of + 5.8. On the other hand we show that if the ratio C _D / C _S is fixed, decreases with C _D with a negative exponent of -2.0. Nevertheless investigations of the zero shear viscosity indicate that in all situations (implying variation of the surfactant concentration C _D , or the salt concentration C _S or the temperature) is a decreasing function of the length of the micelles. All these evolutions are compatible with a gelation mechanism which could possibly be associated with entanglement effects of large interacting flowing structures. Received: 3 March 1998 / Revised: 16 June 1998 / Accepted: 3 July 1998     

A geometric generalization of field theory to manifolds of arbitrary dimension

We introduce a generalization of the O(N) field theory to N-colored membranes of arbitrary inner dimension D. The O(N) model is obtained for , while leads to self-avoiding tethered membranes (as the O(N) model reduces to self-avoiding polymers). The model is studied perturbatively by a 1-loop renormalization group analysis, and exactly as .Freedom to choose the expansion point D, leads to precise estimates of critical exponents of the O(N) model. Insights gained from this generalization include a conjecture on the nature of droplets dominating the 3d-Ising model at criticality; and the fixed point governing the random bond Ising model. Received: 15 October 1998 / Accepted: 4 November 1998     

Charge ordering-disordering in the Th-doped CaMnO3

The structural transitions that appear in the manganites Ca_1-xTh_xMnO₃ versus temperature are studied in connection with their magnetic and transport properties, and compared to those of the Ca_1-xLn_xMnO₃ manganites. An orthorhombic to monoclinic transition is observed for low x values (;this structural distortion, also observed for Ln-doped oxides, is related to the magnetoresistance properties. For higher x values (), modulated commensurate and incommensurate phases are obtained at low temperature, with , b =2 a p and , which are related to Mn³⁺/Mn⁴⁺ charge ordering (CO) phenomena. T values, determined from electron diffraction, are in agreement with those determined from the M ( T ) curves. The low temperature electron microscopy shows that the CO in those oxides is more complex than in Ln-doped manganites. In particular, the destabilisation of CO and consequently of the antiferromagnetic interactions is evidenced as the thorium content increases which may explain the appearance of a spin-glass like behavior for higher x values not seen for Ca_1-xSm_xMnO₃ phases . Received 2 November 1998     

Dynamics of selfavoiding tethered membranes. I. Model A dynamics (Rouse model)

The dynamical scaling properties of selfavoiding polymerized membranes with internal dimension D are studied using model A dynamics. It is shown that the theory is renormalizable to all orders in perturbation theory and that the dynamical scaling exponent z is given by . This result applies especially to membranes (D=2) but also to polymers (D=1). Received: 5 September 1997 / Accepted: 17 November 1997     

Transport theory of multiterminal hybrid structures

We derive a microscopic transport theory of multiterminal hybrid structures in which a superconductor is connected to several spin-polarized electrodes. We discuss the non-perturbative physics of extended contacts, and show that such contacts can be well represented by averaging out the phase of the electronic wave function. The intercontact Andreev reflection and elastic cotunneling conductances are identical if the phase can be averaged out, namely in the presence of at least one extended contact. The maximal conductance of a two-channel contact is proportional to (e ²/h)(a ₀/D)²exp[-D/ξ(ω^*)], where D is the distance between the contacts, a₀ the lattice spacing, ξ(ω) is the superconducting coherence length, and ω^* is the cross-over frequency between a perturbative regime ( ω < ω^*) and a non perturbative regime ( ω^* < ω < Δ). Received 18 June 2001 and Received in final form 17 January 2002     

Nonmonotonic external field dependence of the magnetization in a finite Ising model: Theory and MC simulation

Using field theory and Monte Carlo (MC) simulation we investigate the finite-size effects of the magnetization M for the three-dimensional Ising model in a finite cubic geometry with periodic boundary conditions. The field theory with infinite cutoff gives a scaling form of the equation of state where is the reduced temperature, h is the external field and L is the size of system. Below and at the theory predicts a nonmonotonic dependence of f(x,y) with respect to at fixed and a crossover from nonmonotonic to monotonic behaviour when y is further increased. These results are confirmed by MC simulation. The scaling function f(x,y) obtained from the field theory is in good quantitative agreement with the finite-size MC data. Good agreement is also found for the bulk value at . Received 20 July 1999 and Received in final form 11 November 1999     

Stability and diffusion of surface clusters

Using kinetic Monte Carlo simulations and a bond-counting ansatz, thermal stability and diffusion of an adatom island on a crystal surface are studied. At low temperatures, the diffusion constant D is found to decrease for a wide range of island sizes like , where is close to one, N being the number of adatoms in the cluster. By heating up the surface, the system undergoes a phase transition above which the island disappears. Characteristics of that transition are discussed. Received 20 January 1999     

Levinson's theorem for the Klein-Gordon equation in one dimension

In terms of the modified Sturm-Liouville theorem, the Levinson theorem for the one-dimensional Klein-Gordon equation with a symmetric potential V(x) is established. It is shown that the number N₊ (N_-) of bound states with even (odd) parity is related to the phase shift of the scattering states with the same parity at zero momentum as and The solution of the one-dimensional Klein-Gordon equation with the energy M or -M is called as a half bound state if it is finite but does not decay fast enough at infinity to be square integrable. Received 22 December 1999     

Dynamics of polymeric manifolds in melts: the Hartree approximation

The Martin-Siggia-Rose functional technique and the selfconsistent Hartree approximation is applied to the dynamics of a D-dimensional manifold in a melt of similar manifolds. The generalized Rouse equation is derived and its static and dynamic properties are studied. The static upper critical dimension, d _uc =2D/(2-D), discriminates between Gaussian (or screened) and non-Gaussian regimes, whereas its dynamical counterpart, , discriminates between Rouse- and renormalized-Rouse behavior. The Rouse modes correlation function in a stretched exponential form and the dynamical exponents are calculated explicitly. The special case of linear chains D=1 shows agreement with Monte-Carlo simulations. Received: 22 May 1998 / Received in final form: 31 August 1998 / Accepted: 8 September 1998     

Nanoparticle chain-like formation in electrical double-layered magnetic fluids evidenced by small-angle X-ray scattering

Small-angle X-ray scattering (SAXS) was performed on a series of Electric Double-Layered Magnetic Fluids (EDL-MF) composed of ferrite type-- CoFe₂O₄, MnFe₂O₄, ZnFe₂O₄, NiFe₂O₄ and CuFe₂O₄--nanoparticles of different crystalline sizes ( D _XR ranging from 40 to 139?, as determined by X-ray diffraction). The information concerning the scattering objects was obtained through the analysis of the distance distribution function p(r) and of the size distribution function D(R), both retrieved from SAXS data. The results show that EDL-MF, in the absence of an applied magnetic field, are composed of small magnetic particle aggregates in solution. These agglomerates are elongated in one direction (chain-like) with the longest dimension varying from 240 to 330?. The cross-section size is of the order of D _XR. The data also demonstrate that the maximum dimension of these aggregates is independent of the ferrite type. On the other hand, the number of aggregated magnetic particles is nanoparticle-size-dependent. Accordingly, larger ferrite-type nanoparticles as those with D _XR = 139? form aggregates composed of 2-3 magnetic particles, whereas smaller ones with D _XR 40? form agglomerates of about 6 magnetic particles in solution. As the nanoparticle size is reduced, it might increase the particle surface defects. Such occurrence would affect the particle surface charge density, which could reduce the electrostatic screening, favoring the agglomeration phenomenon. Received 28 February 2000 and Received in final form 28 August 2000     

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     

Born effective charge reversal and metallic threshold state at a band insulator-Mott insulator transition

We study the quantum phase transition between a band (“ionic”) insulator and a Mott-Hubbard insulator, realized at a critical value in a bipartite Hubbard model with two inequivalent sites, whose on-site energies differ by an offset . The study is carried out both in D=1 and D=2 (square and honeycomb lattices), using exact Lanczos diagonalization, finite-size scaling, and Berry's phase calculations of the polarization. The Born effective charge jump from positive infinity to negative infinity previously discovered in D=1 by Resta and Sorella is confirmed to be directly connected with the transition from the band insulator to the Mott insulating state, in agreement with recent work of Ortiz et al. In addition, symmetry is analysed, and the transition is found to be associated with a reversal of inversion symmetry in the ground state, of magnetic origin. We also study the D=1 excitation spectrum by Lanczos diagonalization and finite-size scaling. Not only the spin gap closes at the transition, consistent with the magnetic nature of the Mott state, but also the charge gap closes, so that the intermediate state between the two insulators appears to be metallic. This finding, rationalized within Hartree-Fock as due to a sign change of the effective on-site energy offset for the minority spin electrons, underlines the profound difference between the two insulators. The band-to-Mott insulator transition is also studied and found in the same model in D=2. There too we find an associated, although weaker, polarization anomaly, with some differences between square and honeycomb lattices. The honeycomb lattice, which does not possess an inversion symmetry, is used to demonstrate the possibility of an inverted piezoelectric effect in this kind of ionic Mott insulator. Received 21 May 1999     

Disorder driven roughening transitions of elastic manifolds and periodic elastic media

The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic media, e.g., charge-density waves or flux-line lattices. The competition between both pinning mechanisms leads to a continuous, disorder driven roughening transition between a flat state where the mean relative displacement saturates on large scales and a rough state with diverging relative displacement. The transition can be approached by changing the impurity concentration or, indirectly, by tuning the temperature since the pinning strengths of the random and crystal potential have in general a different temperature dependence. For D dimensional elastic manifolds interacting with either random-field or random-bond disorder a transition exists for 2<D<4, and the critical exponents are obtained to lowest order in . At the transition, the manifolds show a superuniversal logarithmic roughness. Dipolar interactions render lattice effects relevant also in the physical case of D=2. For periodic elastic media, a roughening transition exists only if the ratio p of the periodicities of the medium and the crystal lattice exceeds the critical value . For p<p _c the medium is always flat. Critical exponents are calculated in a double expansion in and and fulfill the scaling relations of random field models. Received 28 August 1998