Comparative study of the critical behavior in one-dimensional random and aperiodic environments

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents . At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as . Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of , whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities. Received: 5 February 1998 / Accepted: 17 April 1998     

Scaling with respect to disorder in time-to-failure

We revisit a simple dynamical model of rupture in random media with long-range elasticity to test whether rupture can be seen as a first-order or a critical transition. We find a clear scaling of the macroscopic modulus as a function of time-to-rupture and of the amplitude of the disorder, which allows us to collapse neatly the numerical simulations over more than five decades in time and more than one decade in disorder amplitude onto a single master curve. We thus conclude that, at least in this model, dynamical rupture in systems with long-range elasticity is a genuine critical phenomenon occurring as soon as the disorder is non-vanishing. Received: 11 July 1997 / Revised: 6 November 1997 / Accepted: 10 November 1997     

Critical phenomena at perfect and non-perfect surfaces

The effect of imperfections on surface critical properties is studied for Ising models with nearest-neighbour ferromagnetic couplings on simple cubic lattices. In particular, results of Monte Carlo simulations for flat, perfect surfaces are compared to those for flat surfaces with random, “weak” or “strong”, interactions between neighbouring spins in the surface layer, and for surfaces with steps of monoatomic height. Surface critical exponents at the ordinary transition, in particular ,are found to be robust against these perturbations. Received: 7 October 1997 / Accepted: 19 November 1997     

Topology invariance in percolation thresholds

An universal invariant for site and bond percolation thresholds ( and respectively) is proposed. The invariant writes where and are positive constants, and d the space dimension. It is independent of the coordination number, thus exhibiting a topology invariance at any d. The formula is checked against a large class of percolation problems, including percolation in non-Bravais lattices and in aperiodic lattices as well as rigid percolation. The invariant is satisfied within a relative error of for all the twenty lattices of our sample at d=2, d=3, plus all hypercubes up to d=6. Received: 7 July 1997 / Accepted: 5 November 1997     

From molecular flexibility to shape, curvature and thermotropic transitions in pure surfaces

A material surface of pure constituents with a flexible molecular chain (amphiphilics) is considered; thermodynamic behaviour is studied in the chain length-temperature plane. The Hamiltonian of the system is modelled as the sum of a formation term which refers to the polymer nature of the chain, and of a fluctuation term with a specific elastic form. For closed systems the model exhibits phases with uniform curvature and conformational order/disorder or, alternatively, modulated phases; a critical chain length is found for the existence of modulated phases; the dependence of transition temperature on energy parameters is determined. A critical region is found for open systems, where conformational disorder drives spontaneous generation of curvature; this lies above a characteristic chain length and around the shape transition temperature. Received: 13 November 1996 / Revised: 9 May 1997 / Received in final form: 4 November 1997 / Accepted: 10 November 1997     

Second-order phase transition induced by deterministic fluctuations in aperiodic eight-state Potts models

We investigate the influence of aperiodic modulations of the exchange interactions between nearest-neighbour rows on the phase transition of the two-dimensional eight-state Potts model. The systems are studied numerically through intensive Monte-Carlo simulations using the Swendsen-Wang cluster algorithm for different aperiodic sequences. The transition point is located through duality relations, and the critical behaviour is investigated using FSS techniques at criticality. While the pure system exhibits a first-order transition, we show that the deterministic fluctuations resulting from the aperiodic coupling distribution are liable to modify drastically the physical properties in the neighbourhood of the transition point. For strong enough fluctuations of the sequence under consideration, a second-order phase transition is induced. The exponents , and are obtained at the new fixed point and crossover effects are discussed. Surface properties are also studied. Received: 18 March 1998 / Revised: 29 June 1998 / Accepted: 10 September 1998     

Universality in three dimensional random-field ground states

We investigate the critical behavior of three-dimensional random-field Ising systems with both Gauss and bimodal distribution of random fields and additional the three-dimensional diluted Ising antiferromagnet in an external field. These models are expected to be in the same universality class. We use exact ground-state calculations with an integer optimization algorithm and by a finite-size scaling analysis we calculate the critical exponents , , and . While the random-field model with Gauss distribution of random fields and the diluted antiferromagnet appear to be in same universality class, the critical exponents of the random-field model with bimodal distribution of random fields seem to be significantly different. Received: 9 July 1998 / Received in final form: 15 July 1998 / Accepted: 20 July 1998     

Adsorption and spreading of polymers at plane interfaces; theory and molecular dynamics simulations

Nonequilibrium processes play a key role in the adsorption kinetics of macromolecules. It is expected that the competition between transport of polymer towards an interface and its subsequent spreading has a significant influence on the adsorbed amount. An increase of the transport rate can lead to an increase of the adsorbed amount, especially when the polymer has too little time to spread at the interface. In this study we present both molecular dynamics simulations and analytical calculations to describe some aspects of the adsorption kinetics. From MD simulations on a poly(ethylene oxide) chain in vacuum near a graphite surface, we conclude that the spreading process can, in first approximation, be described by either a simple exponential function or by first-order reaction kinetics. Combining these spreading models with the transport equations for two different geometries (stagnation-point flow and overflowing cylinder) we are able to derive analytical equations for the adsorption kinetics of polymers at solid-liquid and at liquid-fluid interfaces. Received: 18 July 1997 / Received in final form: 27 October 1997 / Accepted: 6 November 1997     

Novel pattern formation in the collapse process of floating monolayer at the air-water interface

We have observed a remarkable two-armed spiral in the collapse process of a floating monolayer at the air-water interface by phase contrast microscopy. This demonstrates that the floating monolayer as a form of soft condensed matter reorganizes itself due to a certain kind of macroscopic or collective behavior of molecules as it collapses. This pattern formation is caused by the breakdown of a critical dynamical balance between the deformation of solid domain and the applied surface pressure. The fragility as well as the flexibility of the floating monolayer can be associated with the observed pattern growth. There are also observed interesting, periodically arranged collections of molecules in numerous collapsed regions. Received: 8 July 1997 / Accepted: 4 November 1997     

Spin dynamics in hole-doped two-dimensional S = 1/2 Heisenberg antiferromagnets: 63Cu NQR relaxation in La2-xSrxCuO4 for x ≤ 0.04

A cluster algorithm formulated in continuous (imaginary) time is presented for Ising models in a transverse field. It works directly with an infinite number of time-slices in the imaginary time direction, avoiding the necessity to take this limit explicitly. The algorithm is tested at the zero-temperature critical point of the pure two-dimensional (2d) transverse Ising model. Then it is applied to the 2d Ising ferromagnet with random bonds and transverse fields, for which the phase diagram is determined. Finite size scaling at the quantum critical point as well as the study of the quantum Griffiths-McCoy phase indicate that the dynamical critical exponent is infinite as in 1d. Received 6 November 1998     

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     

Canonical dressing in the multimode two-quantum Jaynes-Cummings model

Based upon the hidden Lie SU(1,1) symmetry, we have constructed the unitary decoupling transformation which diagonalizes the multimode two-quantum Jaynes-Cummings model and provides us with an extremely convenient basis to gain a deeper understanding of the dressing processes present in the matter-field interaction. This canonical transformation approach is very simple and can be easily extended to other generalized Jaynes-Cummings models. Received: 5 July 1997 / Revised: 3 November 1997 / Accepted: 14 November 1997     

Multifractal properties of aperiodic Ising model on hierarchical lattices: role of the geometric fluctuations

The role of the geometric fluctuations on the multifractal properties of the local magnetization of aperiodic ferromagnetic Ising models on hierarchical lattices is investigated. The geometric fluctuations are introduced by generalized Fibonacci sequences. The local magnetization is evaluated via an exact recurrent procedure encompassing real space renormalization group decimation. The symmetries of the local magnetization patterns induced by the aperiodic couplings is found to be strongly (weakly) different, with respect to the ones of the corresponding homogeneous systems, when the geometric fluctuations are relevant (irrelevant) to change the critical properties of the system. At the criticality, the measure defined by the local magnetization is found to exhibit a non-trivial F(α) spectra being shifted to higher values of α when relevant geometric fluctuations are considered. The critical exponents are found to be related with some special points of the F(α) function and agree with previous results obtained by the quite distinct transfer matrix approach. Received 2 April 2001 and Received in final form 14 August 2001     

Persistent currents in mesoscopic rings and conformal invariance

The effect of point defects on persistent currents in mesoscopic rings is studied in a simple tight-binding model. Using an analogy with the treatment of the critical quantum Ising chain with defects, conformal invariance techniques are employed to relate the persistent current amplitude to the Hamiltonian spectrum just above the Fermi energy. From this, the dependence of the current on the magnetic flux is found exactly for a ring with one or two point defects. The effect of an aperiodic modulation of the ring, generated through a binary substitution sequence, on the persistent current is also studied. The flux-dependence of the current is found to vary remarkably between the Fibonacci and the Thue-Morse sequences. Received: 4 March 1998 / Revised: 20 April 1998 / Accepted: 30 April 1998     

Mn-site doping induced CMR properties in calcium rich manganites Pr1‒xCaxMnO3(0.6 ≤ x ≤ 0.7)

Doping of Mn-site by chromium, cobalt and nickel has been investigated in the calcium rich manganites and . Whatever the nature of the doping element, a rapid disappearance of the charge ordered (CO) state is observed, decreasing as the doping rate increases. But the most important result concerns the Cr-doped compounds for which a re-entrant insulator to metal transition at 90-120 K is observed for x =0.10-0.12, in a zero magnetic field. The possibility to induce colossal magnetoresistance (CMR) properties for high (IV) contents ((IV)/) for x =0.07-0.12 is shown for the first time, the resistance ratios reaching at 30 K. This study also shows differently that the small size of the A-site cation (Pr, Ca) is not a redhibitory obstacle to the appearance of CMR properties in manganites, in contrast with previously established phase diagrams. Received: 18 June 1997 / Revised: 4 August 1997 / Accepted: 10 November 1997     

Interplay between chains of S = 5/2 localised spins and two-dimensional sheets of organic donors in the synthetically built magnetic multilayer λ ‒ (BETS)2FeCl4

In order to understand the magnetic field-induced restoration of a highly conductive state in , static (SQUID) and dynamic (ESR and AFR) magnetization measurements were performed on polycrystalline samples and single crystals, respectively. In addition, cantilever and resistivity measurements under steady fields were performed. While the metal-insulator transition curve of the () phase diagram exhibits a first order character, a “spin-flop” transition line divides the insulating state when the magnetic field is applied along the easy axis of magnetization. The effects of a RKKY-type indirect exchange and of applied magnetic field are described within the framework of a generalized Kondo lattice, namely two chains of localised spins coupled through the itinerant spins of the 2D sheets of BETS. The calculations, which can incorporate intramolecular electron correlations within a mean field theory, are in qualitative agreement with the field induced transition from the antiferromagnetic insulating ground state to a canted one, i.e. a not fully oriented paramagnetic, but metallic state. Received: 6 August 1997 / Received: 5 November 1997 / Accepted: 10 November 1997     

Axialisation, cooling and quenching of ions in a Penning trap

On the basis of a macroscopic ground state population it was argued recently that Bose-Einstein condensation should occur in a one-dimensional harmonic potential. We examine this situation by drawing analogies to bosons in a two-dimensional box, where the thermodynamic limit is well-defined. We show that in both systems although the ground state populations show sharp onsets at the critical temperature, the behaviour of the specific heat is analytic, which proves the absence of a phase transition in these systems. Received: 17 February 1997 / Revised: 3 September 1997 / Accepted: 13 October 1997     

Transmission of an optical frequency through a 3 km long optical fiber

A 3 km long optical fiber is used to connect two laboratories in Paris. We present the metrological properties of this optical link to transfer an optical frequency standard at 778 nm and we show that the frequency shift introduced by the fiber is only of few Hz. Received: 23 October 1997 / Accepted: 18 November 1997     

Aperiodic extended surface perturbations in the Ising model

We study the influence of an aperiodic extended surface perturbation on the surface critical behaviour of the two-dimensional Ising model in the extreme anisotropic limit. The perturbation decays as a power of the distance l from the free surface with an oscillating amplitude where follows some aperiodic sequence with an asymptotic density equal to 1/2 so that the mean amplitude vanishes. The relevance of the perturbation is discussed by combining scaling arguments of Cordery and Burkhardt for the Hilhorst-van Leeuwen model and Luck for aperiodic perturbations. The relevance-irrelevance criterion involves the decay exponent , the wandering exponent which governs the fluctuation of the sequence and the bulk correlation length exponent . Analytical results are obtained for the surface magnetization which displays a rich variety of critical behaviours in the -plane. The results are checked through a numerical finite-size-scaling study. They show that second-order effects must be taken into account in the discussion of the relevance-irrelevance criterion. The scaling behaviours of the first gap and the surface energy are also discussed. Received 1 December 1998