Phase diagram of randomly polymerized membrane

Using a replica formalism, a generalization of a recent mean field model corresponding to the observed wrinkling transition in randomly polymerized membranes is presented. In this model we study the effects of global fluctuations of the surface normals to the flat membrane, which can be introduced by a random local field. In absence of these global fluctuations, we show that, the model exhibits both continuous and discontinuous transitions between flat and wrinkled phases, contrary to what has been predicted by Bensimon et al. and Attal et al. Phase diagrams both in replica symmetry and in breaking of replica symmetry in sense of Almeida and Thouless are given. We have also investigated the effects of global fluctuations on the replica symmetry phase diagram. We show that, the wrinkled phase is favored and the flat phase is unstable. For large global fluctuations, the transition between wrinkled and flat phases becomes first order. Received: 3 December 1997 / Revised: 31 March 1998 / Accepted: 3 August 1998     

Stability of the Haldane state against the antiferromagnetic-bond randomness

Ground-state phase diagram of the one-dimensional bond-random S=1 Heisenberg antiferromagnet is investigated by means of the loop-cluster-update quantum Monte-Carlo method. The random couplings are drawn from a rectangular uniform distribution. We found that even in the case of extremely broad bond distribution, the magnetic correlation decays exponentially, and the correlation length is hardly changed; namely, the Haldane phase continues to be realized. This result is accordant with that of the exact-diagonalization study, whereas it might contradict the conclusion of an analytic theory founded in a power-law bond distribution instead. The latter theory predicts that a second-order phase transition occurs at a certain critical randomness, and the correlation length diverges for sufficiently strong randomness. Received: 31 March 1998 / Revised and Accepted: 7 July 1998     

The smooth structural change in mesoscopic Peierls chains

We investigate the Peierls transition in finite chains by exact (Lanczos) diagonalization and within a seminumerical method based on the factorization of the electron-phonon wave function (Adiabatic Ansatz, AA). AA can be applied for mesoscopic chains up to micrometer sizes and its reliability can be checked self-consistently. Our study demonstrates the important role played for finite systems by the tunneling in the double well potential. The chains are dimerized only if their size N exceeds a critical value N_c which increases with increasing phonon frequency. Quantum phonon fluctuations yield a broad transition region. This smooth Peierls transition contrasts not only to the sharp mean field transition, but also with the sharp RPA soft mode instability, although RPA partially accounts for quantum phonon fluctuations. For weak coupling the dimerization disappears below micrometer sizes; therefore, this effect could be detected experimentally in mesoscopic systems. Received: 3 January 1998 / Revised: 13 March 1998 / Accepted: 3 April 1998     

Photoemission, inverse photoemission and superconducting correlations in Hubbard and t-J ladders: role of the anisotropy between legs and rungs

Several experiments in the context of ladder materials have recently shown that the study of simple models of anisotropic ladders (i.e. with different couplings along legs and rungs) is important for the understanding of these compounds. In this paper Exact Diagonalization studies of the one-band Hubbard and t-J models are reported for a variety of densities, couplings, and anisotropy ratios. The emphasis is given to the one-particle spectral function which presents a flat quasiparticle dispersion at the chemical potential in some region of parameter space. This is correlated with the existence of strong pairing fluctuations, which themselves are correlated with an enhancement of the bulk-extrapolated value for the two-hole binding energy as well as with the strength of the spin-gap in the hole-doped system. Part of the results for the spectral function are explained using a simple analytical picture valid when the hopping along the legs is small. In particular, this picture predicts an insulating state at quarter filling in agreement with the metal-insulator transition observed at this special filling for increasing rung couplings. The results are compared against previous literature, and in addition pair-pair correlations using extended operators are also here reported. Received: 22 April 1998 / Revised: 23 July 1998 / Accepted: 30 July 1998     

Quantum charge density fluctuations and the phase transition in Ce

We have calculated the quantum quadrupolar interaction due to charge density fluctuations of localized 4f-electrons in Ce by taking into account the angular dependence, the degeneracy of the localized 4f -orbitals and the spin-orbit coupling. The calculated crystal field of 4 f electronic states is in good agreement with neutron diffraction measurements. We show that orientational ordering of quantum quadrupoles drives a phase transition at K which we assign with the transformation. In the phase the centers of mass of the Ce atoms still form a face centered cubic lattice. The theory accounts for the first order character of the transition and for the cubic lattice contraction which accompanies the transition. The transition temperature increases linearly with pressure. Our approach does not involve Kondo spin fluctuations as the significant process for the phase transition. Received 19 October 1998     

On the incommensurate phase in modulated Heisenberg chains

Using the density matrix renormalization group method (DMRG) we calculate the magnetization of frustrated S=1/2 Heisenberg chains for various modulation patterns of the nearest neighbour coupling: commensurate, incommensurate with sinusoidal modulation and incommensurate with solitonic modulation. We focus on the order of the phase transition from the commensurate dimerized phase (D) to the incommensurate phase (I). It is shown that the order of the phase transition depends sensitively on the model. For the solitonic model in particular, a k-dependent elastic energy modifies the order of the transition. Furthermore, we calculate gaps in the incommensurate phase in adiabatic approximation. Received: 9 March 1998 / Accepted: 17 April 1998     

Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor S_ij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region. Received: 28 May 1998 / Revised: 12 August 1998 / Accepted: 8 September 1998     

Electrostatics of DNA-cationic lipid complexes: isoelectric instability

We propose a Poisson-Boltzmann electrostatic theory for DNA/cationic lipid complexes modeled as a stack of aligned DNA chains intercalated with lipid bilayers, a structure suggested by the recent X-ray synchrotron studies of Radler et al. Poisson-Boltzmann theory is shown to predict that the isoelectric point - where the DNA and cationic lipid charges are in balance - is unstable against absorption of extra DNA or lipid material. The instability is caused by the entropy gain obtained following the release of small ions inside the complex and is manifested by singular behavior of the rod-rod spacing near the isoelectric point. We apply the theory to a discussion of the results of Radler et al. Received: 21 July 1997 / Received in final form: 19 January 1998 /Accepted: 5 March 1998     

Structure and rheology of concentrated wormlike micelles [4]at the shear-induced isotropic-to-nematic transition

We have investigated the simple shear flow behavior of wormlike micelles using small-angle neutron scattering and mechanical measurements. Ternary surfactant solutions made of cetylpyridinium chloride, hexanol and brine (0.2 M NaCl) and hereafter abbreviated as CPCl-Hex were studied in the concentrated regime, . In a preliminary report (Berret et al. [#!ref16!#]), the discontinuity of slope observed in the shear stress versus shear rate curve was interpreted in terms of first-order phase transition between an isotropic state and a shear-induced nematic state ( transition). At the transition rate, , the solution exhibits a macroscopic phase separation into viscous and fluid layers (inhomogeneous shear flow). Above a second characteristic shear rate, the flow becomes homogeneous again, the sheared solution being nematic only. The neutron patterns obtained in the two-state inhomogeneous region have been re-examined. Based on a consistent analysis of both orientational and translational degrees of freedom related to the wormlike micelles, we emphasize new features for the transition. In the present paper, the shear rate variations of the relative proportions of each phase in the two-state region, as well as the viscosity ratio between isotropic and nematic phases are derived. We demonstrate in addition that slightly above the transition rate, the shear induced nematic phase is already strongly oriented, with an order parameter P ₂ = 0.65. The orientational state is that of a nematic flow-oriented monodomain. Finally, from the locations of the neutron scattering maxima for each isotropic and nematic contributions, we evaluate the concentrations for each phase and and derived a dynamical phase diagram of CPCl-Hex, in terms of the stress versus and . According to the classification by Schmitt et al. [#!ref22!#], the transition observed in CPCl-Hex micellar solutions could result from a positive flow-concentration coupling, in agreement with the observed monotonically increasing shear stress in the two-phase region. Received: 16 February 1998 / Revised: 18 February 1998 / Accepted: 24 May 1998     

Surface effects in field-induced smectic transitions

We study the surface behavior of a semi-infinite smectogenic sample bounded by a solid wall, in the presence of an external electric field. Our analysis is performed in the framework of a Landau-de Gennes theory. For the sake of simplicity, we consider only the case in which, in the absence of field and surfaces, a direct isotropic to smectic-A transition occurs, while in the presence of the electric field a nonspontaneous nematic phase appears. Two new surface phases are identified, namely a parasmectic and a surface-induced smectic phase. The shifts in the transition temperatures and the critical behavior of the surface states are analyzed. Received: 25 August 1997 / Accepted: 23 January 1998     

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     

Van der Waals interaction between flux lines in high- superconductors: A variational approach

In pure anisotropic or layered superconductors thermal fluctuations induce a van der Waals attraction between flux lines. This attraction together with the entropic repulsion has interesting consequences for the low field phase diagram; in particular, a first order transition from the Meissner phase to the mixed state is induced. We introduce a new variational approach that allows for the calculation of the effective free energy of the flux line lattice on the scale of the mean flux line distance a, which is based on an expansion of the free energy around the regular triangular Abrikosov lattice. Using this technique, the low field phase diagram of these materials may be explored. The results of this technique are compared with a recent functional RG treatment of the same system. Received: 25 June 1996 / Revised: 18 August 1998 / Accepted: 21 August 1998     

Universal scaling properties of extreme type-II superconductors in magnetic fields

Anisotropic Ginzburg-Landau superconductors of extreme type-II are considered in an approximation where magnetic field fluctuations are neglected. A formulation of the scaling properties is presented for the singular part of the free energy density in the presence of a magnetic field. From the existence of a magnetization, a diamagnetic susceptibility and superconductivity we determine the limiting behavior of the scaling function in the vicinity of the zero field transition temperature, where critical fluctuations dominate. Our predictions for the temperature and field dependence of magnetization, magnetic torque and melting line etc., uncover the universal critical properties and provide an extension of hitherto used mean-field treatments. The results are consistent with experimental data. Received: 24 April 1998 / Accepted: 5 May 1998     

Singularity of the specific heat of two-dimensional random Ising models

The singularity of the specific heat is studied for the dilution (J>J'>0) type and Gaussian type random Ising models using the Pfaffian method numerically. The type of singularity at the paramagnetic-ferromagnetic phase boundary is studied using the standard regression method using data up to system size. It is shown that the logarithmic type singularity is more reliable than the double-logarithmic type and cusp type singularities. The critical temperatures are estimated accurately for both the dilution type and Gaussian type random Ising models. A phase diagram relating strength of the randomness and temperature is also presented. Received: 26 February 1998 / Revised: 15 May 1998 / Accepted: 25 June 1998     

The effect of DNA phase structure on DNA walks

We have performed several kinds of DNA walks which often are the first steps for further analysis of DNA structure and long range correlations. The DNA walks analysing frequency of G+C versus A+T cannot indicate the coding strand while purine versus pyrimidine DNA walks or two-dimensional (A-T,G-C) DNA walks in some instances can indicate the coding strand but cannot resolve the coding frame. The modified two-dimensional (A-T,G-C) DNA walks respecting the three-nucleotide codon structure show very high correlation in nucleotide composition of DNA coding sequences. They can distinguish between coding and non-coding sequences and indicate the strand and the phase in which DNA is coding. Received: 8 January 1998 / Received in final form and Accepted: 28 January 1998     

Mixed spin transverse Ising model with longitudinal random crystal field interactions

The effect of a longitudinal random crystal field interaction on the phase diagrams of the mixed spin transverse Ising model consisting of spin-1/2 and spin-1 is investigated within the finite cluster approximation based on a single-site cluster theory. In order to expand a cluster identity of spin-1, we transform the spin-1 to spin-1/2 representation containing Pauli operators. We derive the state equations applicable to structures with arbitrary coordination number N. The phase diagrams obtained in the case of a honeycomb lattice (N=3) and a simple-cubic lattice (N=6), are qualitatively different and examined in detail. We find that both systems exhibit a variety of interesting features resulting from the fluctuation of the crystal field interactions. Received: 13 February 1998 / Accepted: 17 March 1998     

First and second order transition in frustrated XY systems

The nature of the phase transition for the XY stacked triangular antiferromagnet (STA) is a controversial subject at present. The field theoretical renormalization group (RG) in three dimensions predicts a first order transition. This prediction disagrees with Monte-Carlo (MC) simulations which favor a new universality class or a tricritical transition. We simulate by the Monte-Carlo method two models derived from the STA by imposing the constraint of local rigidity which should have the same critical behavior as the original model. A strong first order transition is found. Following Zumbach we analyze the second order transition observed in MC studies as due to a fixed point in the complex plane. We review the experimental results in order to clarify the critical behavior observed. Received: 18 February 1998 / Revised: 24 April 1998 / Accepted: 30 April 1998     

Statistical analysis of the transition to turbulence in plane Couette flow

We argue on general grounds that the transition to turbulence in plane Couette flow is best studied experimentally at a statistical level. We present such a statistical analysis of experimental data guided by a parallel investigation of a simple coupled map lattice model for spatiotemporal intermittency. We confirm that this generic type of spatiotemporal chaos is relevant in the context of plane Couette flow, where the linear stability of the laminar regime at all Reynolds numbers insures the necessary local subcriticality. Using large ensembles of similar experiments, we show the existence of a well-defined threshold Reynolds number above which a unique, turbulent, intermittent attractor coexists with the laminar flow. Furthermore, our data reveals that this transition to spatiotemporal intermittency is discontinuous, i.e. akin to a first-order phase transition. Received: 10 April 1998 / Revised: 22 June 1998 / Accepted: 24 June 1998     

Langevin dynamics of the glass forming polymer melt: Fluctuations around the random phase approximation

In this paper the Martin-Siggia-Rose (MSR) functional integral representation is used for the study of the Langevin dynamics of a polymer melt in terms of collective variables: mass density and response field density. The resulting generating functional (GF) takes into account fluctuations around the random phase approximation (RPA) up to an arbitrary order. The set of equations for the correlation and response functions is derived. It is generally shown that for cases whenever the fluctuation-dissipation theorem (FDT) holds we arrive at equations similar to those derived by Mori-Zwanzig. The case when FDT in the glassy phase is violated is also qualitatively considered and it is shown that this results in a smearing out of the ideal glass transition. The memory kernel is specified for the ideal glass transition as a sum of all “water-melon” diagrams. For the Gaussian chain model the explicit expression for the memory kernel was obtained and discussed in a qualitative link to the mode-coupling equation. Received: 9 January 1998 / Revised: 24 April 1998 / Accepted: 2 July 1998