The Bethe lattice spin glass revisited

So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non perturbative solution of the Bethe lattice spin glass problem at a level of approximation which is equivalent to a one step replica symmetry breaking solution. The results compare well with numerical simulations. The method can be used for many finite connectivity problems appearing in combinatorial optimization. Received 27 September 2000     

Aging dynamics of Edwards-Anderson spin glasses

We analyze by means of extensive computer simulations the out of equilibrium dynamics of Edwards-Anderson spin glasses in d = 4 and d = 6 dimensions with ± J interactions. In particular, we focus our analysis on the scaling properties of the two-time autocorrelation function in a wide range of temperatures from T = 0.07 T _c to T = 0.75 T _c in both systems. In both the 4 d and 6 d models at very low temperatures we study the effects of discretization of energy levels. Strong sub-aging behaviors are found. We argue that this is because in the times accessible to our simulations the systems are only able to probe activated dynamics through the lowest discrete energy levels and remain trapped around nearly flat regions of the energy landscape. For temperatures T ≥ 0.5 T _c in 4 d and 6 d we find logarithmic scalings that are compatible with simple dynamical ultrametricity. Nevertheless the behaviour of the systems, even in 6 d is very different from the mean field SK model results. Received 21 October 2002 / Received in final form 13 January 2003 Published online 11 April 2003 RID="a" ID="a"Associate researcher of the Abdus Salam International Centre for Theoretical Physics; e-mail: stariolo@if.ufrgs.br; http://www.if.ufrgs.br/stariolo RID="b" ID="b"Present address: The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy e-mail: mmontemu@ictp.trieste.it RID="c" ID="c"e-mail: tamarit@famaf.unc.edu.ar     

Ultrametricity between states at different temperatures in spin-glasses

We prove the existence of correlations between the equilibrium states at different temperatures of the multi-p-spin spherical spin-glass models with continuous replica symmetry breaking: there is no chaos in temperature in these models. Furthermore, the overlaps satisfy ultrametric relations. As a consequence the Parisi tree is essentially the same at all temperatures with lower branches developing when lowering the temperature. We conjecture that the reference free energies of the clusters are also fixed at all temperatures as in the generalized random-energy model. Received 18 March 2002 / Received in final form 14 June 2002 Published online 1st October 2002 RID="a" ID="a"e-mail: tommaso.rizzo@inwind.it     

The <Emphasis Type="Bold">±</Emphasis><Emphasis Type="Bold">J</Emphasis> spin glass in Migdal-Kadanoff approximation

We study the low-temperature phase of the three-dimensional ± J Ising spin glass in Migdal-Kadanoff approximation. At zero temperature, T = 0, the properties of the spin glass result from the ground-state degeneracy and can be elucidated using scaling arguments based on entropy. The approach to the asymptotic scaling regime is very slow, and the correct exponents are only visible beyond system sizes around 64. At T > 0, a crossover from the zero-temperature behaviour to the behaviour expected from the droplet picture occurs at length scales proportional to T ^-2/ds where d_s is the fractal dimension of a domain wall. Canonical droplet behaviour is not visible at any temperature for systems whose linear dimension is smaller than 16 lattice spacings, because the data are either affected by the zero-temperature behaviour or the critical point behaviour. Received 18 February 2001     

Comparing mean field and Euclidean matching problems

Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional systems. Our focus here is on minimum matching problems, because they are computationally tractable while both frustrated and disordered. We first study a mean field model taking the link lengths between points to be independent random variables. For this model we find perfect agreement with the results of a replica calculation, and give a conjecture. Then we study the case where the points to be matched are placed at random in a d-dimensional Euclidean space. Using the mean field model as an approximation to the Euclidean case, we show numerically that the mean field predictions are very accurate even at low dimension, and that the error due to the approximation is O(1/d ² ). Furthermore, it is possible to improve upon this approximation by including the effects of Euclidean correlations among k link lengths. Using k=3 (3-link correlations such as the triangle inequality), the resulting errors in the energy density are already less than at . However, we argue that the dimensional dependence of the Euclidean model's energy density is non-perturbative, i.e., it is beyond all orders in k of the expansion in k-link correlations. Received: 1st December 1997 / Revised: 6 May 1998 / Accepted: 30 June 1998     

Comment on “Growth of Molecular Superlattice in Fully Hydrated Dipalmitoylphosphatidylcholine during Subgel Phase Formation Process” by H. Takahashi, K. Hatta and I. Hatta

This comment shows that data recently reported [#!ref1!#] as being seemingly in conflict with earlier data [#!ref2!#] are, in fact, in excellent agreement. Together, both studies confirm that the kinetics of the subgel phase transformation in dipalmitoylphosphatidylcholine (DPPC) lipid bilayers obeys Kolmogorov-Avrami (K-A) theory [#!ref3!#,#!ref4!#] with an anomalously low effective dimensionality. Received: 11 December 1997 / Accepted: 28 January 1998     

Non-equilibrium dynamics of simple spherical spin models

We investigate the non-equilibrium dynamics of spherical spin models with two-spin interactions. For the exactly solvable models of the d-dimensional spherical ferromagnet and the spherical Sherrington-Kirkpatrick (SK) model the asymptotic dynamics has for large times and large waiting times the same formal structure. In the limit of large waiting times we find in both models an intermediate time scale, scaling as a power of the waiting time with an exponent smaller than one, and thus separating the time-translation-invariant short-time dynamics from the aging regime. It is this time scale on which the fluctuation-dissipation theorem is violated. Aging in these models is similar to that observed in spin glasses at the level of correlation functions, but different at the level of response functions, and thus different at the level of experimentally accessible quantities like thermoremanent magnetization. Received 22 April 1999     

Scattering from solutions of star polymers

We study the scattering intensity of dilute and semi-dilute solutions of star polymers. The star conformation is described by a model introduced by Daoud and Cotton. In this model, a single star is regarded as a spherical region of a semi-dilute polymer solution with a local, position dependent screening length. For high enough concentrations, the outer sections of the arms overlap and build a semi-dilute solution (a sea of blobs) where the inner parts of the actual stars are embedded. The scattering function is evaluated following a method introduced by Auvray and de Gennes. In the dilute regime there are three regions in the scattering function: the Guinier region (low wave vectors, ) from where the radius of the star can be extracted; the intermediate region () that carries the signature of the form factor of a star with f arms: ; and a high wavevector zone () where the local swollen structure of the polymers gives rise to the usual q ^-5/3 decay. In the semi-dilute regime the different stars interact strongly, and the scattered intensity acquires two new features: a liquid peak that develops at a reciprocal position corresponding to the star-star distances; and a new large wavevector contribution of the form q ^-5/3 originating from the sea of blobs. Received: 3 September 1997 / Revised: 13 January 1988 / Accepted: 31 March 1998     

Large-scale low-energy excitations in 3-d spin glasses

We numerically extract large-scale excitations above the ground state in the 3-dimensional Edwards-Anderson spin glass with Gaussian couplings. We find that associated energies are O(1), in agreement with the mean field picture. Of further interest are the position-space properties of these excitations. First, our study of their topological properties show that the majority of the large-scale excitations are sponge-like. Second, when probing their geometrical properties, we find that the excitations coarsen when the system size is increased. We conclude that either finite size effects are very large even when the spin overlap q is close to zero, or the mean field picture of homogeneous excitations has to be modified. Received 14 August 2000     

The statistical mechanics of turbo codes

The “turbo codes”, recently proposed by Berrou et al. [1] are written as a disordered spin Hamiltonian. It is shown that there exists a threshold such that for signal to noise ratios the error probability per bit vanishes in the thermodynamic limit, i.e. the limit of infinitely long sequences. The value of the threshold has been computed for two particular turbo codes. It is found that it depends on the code. These results are compared with numerical simulations. Received 14 March 2000 and Received in final form 17 July 2000     

Turbo codes: the phase transition

Turbo codes are a very efficient method for communicating reliably through a noisy channel. There is no theoretical understanding of their effectiveness. In reference [1] they are mapped onto a class of disordered spin models. The analytical calculations concerning these models are reported here. We prove the existence of a no-error phase and compute its local stability threshold. As a byproduct, we gain some insight into the dynamics of the decoding algorithm. Received 14 March 2000     

Numerical diagonalization analysis of the ground-state superfluid-localization transition in two dimensions

Ground state of the two-dimensional hard-core-boson system in the presence of the quenched random chemical potential is investigated by means of the exact-diagonalization method for the system sizes up to L=5. The criticality and the DC conductivity at the superfluid-localization transition have been controversial so far. We estimate, with the finite-size scaling analysis, the correlation-length and the dynamical critical exponents as and z=2, respectively. The AC conductivity is computed with the Gagliano-Balseiro formula, with which the resolvent (dynamical response function) is expressed in terms of the continued-fraction form consisting of Lanczos tri-diagonal elements. Thereby, we estimate the universal DC conductivity as . Received 19 August 1998     

The kinetic spin-1 Blume-Capel model with competing dynamics

We have studied by means of Monte-Carlo simulation and exact finite-size analysis, the spin-1 Blume Capel model with Glauber and Kawasaki dynamics. The Kawasaki spin-exchange process transfers energy into the system from an external source. Some phase diagrams of the model are presented. For some parameter values, the system displays a kind of self-organization phenomenon within the disordered phase. Received 15 February 2000     

Suppression of antiferromagnetic correlations by quenched dipole-type impurities

The effects of quenched dipole moments on a two-dimensional Heisenberg antiferromagnet are found exactly, by applying the renormalization group to the appropriate classical non-linear sigma model. Such dipole moments represent random fields with power law correlations. At low temperatures, they also represent the long range effects of quenched random strong ferromagnetic bonds on the antiferromagnetic correlation length, , of a two-dimensional Heisenberg antiferromagnet. It is found that the antiferromagnetic long range order is destroyed for any non-zero concentration, x, of the dipolar defects, even at zero temperature. Below a line , where T is the temperature, is independent of T, and decreases exponentially with x. At higher temperatures, it decays exponentially with , with an effective stiffness constant , which decreases with increasing x/T. The latter behavior is the same as for annealed dipole moments, and we use our quenched results to interpolate between the two types of averaging for the problem of ferromagnetic bonds in an antiferromagnet. The results are used to estimate the three-dimensional Néel temperature of a lamellar system with weakly coupled planes, which decays linearly with x at small concentrations, and drops precipitously at a critical concentration. These predictions are shown to reproduce successfully several of the prominent features of experiments on slightly doped copper oxides. Received 22 October 1998     

Theory of site-disordered magnets

In realistic spinglasses, such as , and , magnetic atoms are located at random positions. Their couplings are determined by their relative positions. For such systems a field theory is formulated. In certain limits it reduces to the Hopfield model, the Sherrington-Kirkpatrick model, and the Viana-Bray model. The model has a percolation transition, while for RKKY couplings the “concentration scaling” occurs. Within the Gaussian approximation the Ginzburg-Landau expansion is considered in the clusterglass phase, that is to say, for not too small concentrations. Near special points, the prefactor of the cubic term, or the one of the replica-symmetry-breaking quartic term, may go through zero. Around such points new spin glass phases are found. Received: 27 April 1998 / Received in final form: 27 July 1998 / Accepted: 13 August 1998     

Phase diagram of the 3D bimodal random-field Ising model

The one-parametric Wang-Landau (WL) method is implemented together with an extrapolation scheme to yield approximations of the two-dimensional (exchange-energy, field-energy) density of states (DOS) of the 3D bimodal random-field Ising model (RFIM). The present approach generalizes our earlier WL implementations, by handling the final stage of the WL process as an entropic sampling scheme, appropriate for the recording of the required two-parametric histograms. We test the accuracy of the proposed extrapolation scheme and then apply it to study the size-shift behavior of the phase diagram of the 3D bimodal RFIM. We present a finite-size converging approach and a well-behaved sequence of estimates for the critical disorder strength. Their asymptotic shift-behavior yields the critical disorder strength and the associated correlation length's exponent, in agreement with previous estimates from ground-state studies of the model.     

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     

Fluctuation-magnification of non-equilibrium membranes near a wall

Membranes in thermal equilibrium are well known to exhibit Brownian motion type shape fluctuations. Membranes containing active force centers -- such as chemically active membrane proteins -- suffer additional non-equilibrium shape fluctuations due to the activity of these force centers. We demonstrate, using scaling arguments, that non-equilibrium shape fluctuations are in general greatly amplified by the presence of a nearby wall or membrane due to the absence of a fluctuation-dissipation theorem. For adhesive membranes, this fluctuation magnification effect may facilitate the establishment of bonding. For non-adhesive membranes, fluctuation magnification produces a long-range repulsive pressure which can exceed the well known Helfrich repulsion due to purely thermal fluctuations. Received: 1 September 1997 / Accepted: 3 December 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     

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