Violation of finite-size scaling in three dimensions

We reexamine the range of validity of finite-size scaling in the lattice model and the field theory below four dimensions. We show that general renormalization-group arguments based on the renormalizability of the theory do not rule out the possibility of a violation of finite-size scaling due to a finite lattice constant and a finite cutoff. For a confined geometry of linear size L with periodic boundary conditions we analyze the approach towards bulk critical behavior as at fixed for where is the bulk correlation length. We show that for this analysis ordinary renormalized perturbation theory is sufficient. On the basis of one-loop results and of exact results in the spherical limit we find that finite-size scaling is violated for both the lattice model and the field theory in the region . The non-scaling effects in the field theory and in the lattice model differ significantly from each other. Received 5 February 1999     

Eden growth model for aggregation of charged particles

The stochastic Eden model of charged particles aggregation in two-dimensional systems is presented. This model is governed by the following two parameters: screening length of electrostatic interaction, , and short-range attraction energy, E. Different patterns of finite and infinite aggregates are observed. They are of the following morphology types: linear or linear with bending, worm-like, DBM (dense-branching morphology), DBM with nucleus, and compact Eden-like. The transition between the different modes of growth is studied and phase diagram of the growth structures is obtained in co-ordinates. The detailed aggregate structure analysis, including analysis of their scaling properties, is presented. The scheme of the internal inhomogeneous structure of aggregates is proposed. Received 2 September 1998 and Received in final form 15 January 1999     

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     

Thermoelastic behaviour of polyvinylacetate monolayers at the air-water interface: Evidences for liquid-solid phase transition

The thermoelastic behaviour of polyvinylacetate monolayers spread on an aqueous subphase has been studied using rheological data previously published (Monroy et al., Phys. Rev. E 58, 7629 (1998)). The results show fluid-like viscoelastic behaviour well above a transition temperature , while at lower temperatures a soft solid-like behaviour emerges. The correlation between thermodynamic and elastic properties below can be described in terms of scaling laws. Received 12 January 1999 and Received in final form 11 June 1999     

Conserved dynamics and interface roughening in spontaneous imbibition: A phase field model

The propagation and roughening of a fluid-gas interface through a disordered medium in the case of capillary driven spontaneous imbibition is considered. The system is described by a conserved (model B) phase-field model, with the structure of the disordered medium appearing as a quenched random field . The flow of liquid into the medium is obtained by imposing a non-equilibrium boundary condition on the chemical potential, which reproduces Washburn's equation for the slowing down motion of the average interface position H. The interface is found to be superrough, with global roughness exponent , indicating anomalous scaling. The spatial extent of the roughness is determined by a length scale arising from the conservation law. The interface advances by avalanche motion, which causes temporal multiscaling and qualitatively reproduces the experimental results of Horv'ath and Stanley (Phys. Rev. E 52, 5166 (1995)) on the temporal scaling of the interface. Received 24 November 1999     

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     

Is there a universality of the helix-coil transition in protein models?

The similarity in the thermodynamic properties of two completely different theoretical models for the helix-coil transition is examined critically. The first model is an all-atomic representation for a poly-alanine chain, while the second model is a minimal helix-forming model that contains no system specifics. Key characteristics of the helix-coil transition, in particular, the effective critical exponents of these two models agree with each other, within a finite-size scaling analysis. Received 8 December 1999     

Chain length dependence of anomalous swelling in multilamellar lipid vesicles

Using small-angle X-ray scattering, the repeat distance vs. temperature is measured for a homologous series of multilamellar vesicles of lecithins with varying acyl chain length in excess water condition around the lipid main transition. A systematic chain length dependence is found which is in accordance with a bending rigidity renormalization and critical unbinding of the lamellae close to the transition, as previously suggested in H?nger et al. [Phys. Rev. Lett. 72, 3911 (1994)]. Received 13 January 1999 and Received in final form 6 September 1999     

Time distribution and loss of scaling in granular flow

Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling p) and deterministic critical slope processes with internal correlation time t_c equal to the avalanche lifetime, in model A, and ,in model B. In both cases nonuniversal scaling properties of avalanche distributions are found for , where is related to directed percolation threshold in d=3. Distributions of avalanche durations for are studied in detail, exhibiting multifractal scaling behavior in model A, and finite size scaling behavior in model B, and scaling exponents are determined as a function of p. At a phase transition to noncritical steady state occurs. Due to difference in the relaxation mechanisms, avalanche statistics at approaches the parity conserving universality class in model A, and the mean-field universality class in model B. We also estimate roughness exponent at the transition. Received: 29 May 1998 / Revised: 8 September 1998 / Accepted: 10 September 1998     

Short-time behavior of the kinetic spherical model with long-ranged interactions

The kinetic spherical model with long-ranged interactions and an arbitrary initial order m₀ quenched from a very high temperature to T is solved. In the short-time regime, the bulk order increases with a power law in both the critical and phase-ordering dynamics. To the latter dynamics, a power law for the relative order is found in the intermediate time-regime. The short-time scaling relations of small m₀ are generalized to an arbitrary m₀ and all the time larger than . The characteristic functions for the scaling of m₀ and for are obtained. The crossover between scaling regimes is discussed in detail. Received 17 September 1999     

Ageing of random porous media following fluid deterministic displacement, freezing, thawing

This paper introduces and investigates a simple model of random porous media degradation via several fluid displacing, freezing, and thawing cycles. The fluid transport is based on the deterministic method. The result shows that the topology and the geometry of porous media have a strong effect on displacement processes. The cluster size of the viscous fingering (VF) pattern in the percolation cluster increases with the increase of iteration parameter n. When iteration parameter , the VF pattern does not change with n. When and , the peak value of the distribution increases as n increases; is the normalized distribution of throat sizes after different displacement-damage but before the freezing. The distribution of throat size N(r) after displacement but before freezing damage, shows that the major change, after successive cycles, happens at r>0.9. The peak value of the distribution reaches a maximum when and r=1, where is the normalized distribution of the size of invaded throats for different iterations. This result is different from invasion percolation. The distribution of velocities normal to the interface of VF in the percolation cluster is also studied. When , the scaling function distribution is very sharp. The sweep efficiency E increases along with the increasing of iteration parameter n and decreases with the network size L. And E has a minimum as L increases to the maximum size of the lattice. The VF pattern in the percolation cluster has one frozen zone and one active zone. Received 30 March 1999 and Received in final form 8 August 1999     

Scaling behaviour in the fracture of fibrous materials

We study the existence of distinct failure regimes in a model for fracture in fibrous materials. We simulate a bundle of parallel fibers under uniaxial static load and observe two different failure regimes: a catastrophic and a slowly shredding. In the catastrophic regime the initial deformation produces a crack which percolates through the bundle. In the slowly shredding regime the initial deformations will produce small cracks which gradually weaken the bundle. The boundary between the catastrophic and the shredding regimes is studied by means of percolation theory and of finite-size scaling theory. In this boundary, the percolation density scales with the system size L, which implies the existence of a second-order phase transition with the same critical exponents as those of usual percolation. Received 24 June 1999     

Self-assembly and structure transformations in living polymers forming fibrils

The classical isodesmic one-dimensional model for equilibrium polymerization is generalized in order to describe self-assembly in systems forming fibrils. The model was applied to peptide solutions forming -sheet tapes which can further aggregate into stacks of various thickness: double tapes and fibrils (several double tapes stacked together). We found that in some cases the model yields several step-like transitions as the concentration increases: first from monomers to single or double tapes, and then to fibrils. The abruptness of the first transition is controlled by the free energy penalty for transformation of a peptide from random coil to a straight -strand conformation (the latter is characteristic for tapes). If both single and double tapes are allowed, the length of the aggregates after the first transition can be very large with high scission energies. For very low energies of attraction between double tapes, the transition from double tapes to fibrils happens separately (above the first transition), and it is even more abrupt and produces extremely long fibrils. The theoretical findings are used to extract the characteristic molecular parameters for the self-assembly of the de novo peptide DN1 forming polymeric -sheets in water. Received 28 June 1999     

Scaling properties of dynamic response in orientational glasses

The freezing transition in dipolar and quadrupolar glasses is characterized by the presence of local random electric and strain fields generated by substitutional disorder. The dynamic response in the ergodic phase above the freezing temperature T_F is studied in terms of Langevin dynamics applied to the recently formulated symmetry-adapted random-bond-random-field (SARBRF) model of orientational glasses. Following the theory of spin glasses it is assumed that for T≥T_F the response can be written in a dynamic scaling form by introducing a scaling exponent v and a frequency scaling variable. The value of v(T) is explicitly evaluated for the quadrupolar (100) SARBRF model, and its relation to the experimentally observed effective exponent u_eFF(T) in dipolar and quadrupolar glasses is discussed.     

Zero-temperature TAP equations for the Ghatak-Sherrington model

The zero-temperature TAP equations for the spin-1 Ghatak-Sherrington model are investigated. The spin-glass energy density (ground state) is determined as a function of the anisotropy crystal field D for a large number of spins. This allows us to locate a first-order transition between the spin-glass and paramagnetic phases within a good accuracy. The total number of solutions is also determined as a function of D. Received 25 November 1999     

Predissociation resonances in CO and IBr. Smooth exterior scaling combined with the discrete variable representation

Smooth exterior scaling (SES) and the discrete variable representation (DVR) are combined to accurately compute predissociation resonances of a bound state non-adiabatically coupled to a dissociative state. For the CO( predissociation interaction good agreement is found with approaches based on optical potentials and complex scaling. The comparison is done both in the diabatic and the adiabatic representation. The effect of the coupling strength in the IBr predissociation interaction and the transition from the diabatic to the adiabatic picture was studied by computing resonances for coupling strengths from up to . The transition from weak (diabatic) to strong (adiabatic) coupling was clearly seen. The intermediate case leads to a complicated resonance distribution. Comparison was made with recent studies using pump-probe spectroscopy [M. Shapiro, M.J.J. Vrakking, A. Stolow, J. Chem. Phys. 110, 2465 (1999)]. It was found that the overall features of the experiment could be explained from the resonance distribution, but for a detailed comparison more accurate potential energy surfaces and couplings are needed. Received 12 July 1999 and Received in final form 6 December 1999     

Effect of hydrodynamic flow on kinetics of nematic-isotropic transition in liquid crystals

We investigate kinetics of nematic-isotropic transition by solving the hydrodynamic equations for the nematic tensor order parameter and the fluid velocity in two space dimension (x-y plane). Numerical results indicate that nematic directors tend to align parallel to the x-y plane when hydrodynamic flow is incorporated. Late stage growth exponents, for the correlation length and for the number of topological defects, are not significantly altered by hydrodynamic flow. However, in contrast to the case without flow, the relation holds well, which may indicate the validity of dynamical scaling for the case with hydrodynamic flow. Received: 8 September 1997 / Received in final form: 23 October 1997 /Accepted: 3 November 1997