3D Spin Glass and 2D Ferromagnetic XY Model: a Comparison

We compare the probability distributions and Binder cumulants of the overlap in the 3D Ising spin glass with those of the magnetization in the ferromagnetic 2D XY model. We analyze similarities and differences. Evidence for the existence of a phase transition in the spin glass model is obtained thanks to the crossing of the Binder cumulant. We show that the behavior of the XY model is fully compatible with the Kosterlitz-Thouless scenario. Finite size effects have to be dealt with by using great care in order to discern among two very different physical pictures that can look very similar if analyzed without large attention.Comment: 14 pages and 6 figures. Also available at http://chimera.roma1.infn.it/index_papers_complex.htm

Lennard-Jones binary mixture: a thermodynamical approach to glass transition

We study the liquid-glass transition of the Lennard-Jones binary mixture introduced by Kob and Andersen from a thermodynamic point of view. By means of the replica approach, translating the problem in the study of a molecular liquid, we study the phase transition due to the entropy crisis and we find that the Kauzmann's temperature \tk is $\sim 0.32$. At the end we compare analytical predictions with numerical results.Comment: 24 pages, 11 postscript figures. Revised version accepted for pubblication on J. Chem. Phys. Numerical precision of the computations improve

New evidence for super-roughening in crystalline surfaces with disordered substrate

We study the behavior of the Binder cumulant related to long distance correlation functions of the discrete Gaussian model of disordered substrate crystalline surfaces. We exhibit numerical evidence that the non-Gaussian behavior in the low-$T$ region persists on large length scales, in agreement with the broken phase being super-rough.Comment: 10 pages and 4 figures, available at http://chimera.roma1.infn.it/index_papers_complex.html . We have extended the RG discussion and minor changes in the tex

Inferring DNA sequences from mechanical unzipping: an ideal-case study

We introduce and test a method to predict the sequence of DNA molecules from in silico unzipping experiments. The method is based on Bayesian inference and on the Viterbi decoding algorithm. The probability of misprediction decreases exponentially with the number of unzippings, with a decay rate depending on the applied force and the sequence content.Comment: Source as TeX file with ps figure

A Solvable Model of a Glass

An analytically tractable model is introduced which exhibits both, a glass--like freezing transition, and a collection of double--well configurations in its zero--temperature potential energy landscape. The latter are generally believed to be responsible for the anomalous low--temperature properties of glass-like and amorphous systems via a tunneling mechanism that allows particles to move back and forth between adjacent potential energy minima. Using mean--field and replica methods, we are able to compute the distribution of asymmetries and barrier--heights of the double--well configurations {\em analytically}, and thereby check various assumptions of the standard tunneling model. We find, in particular, strong correlations between asymmetries and barrier--heights as well as a collection of single--well configurations in the potential energy landscape of the glass--forming system --- in contrast to the assumptions of the standard model. Nevertheless, the specific heat scales linearly with temperature over a wide range of low temperatures.Comment: 11 pages, latex, including 5 figures, talk presented at the XIV Sitges Conferenc

Finite-temperature ordering in a two-dimensional highly frustrated spin model

We investigate the classical counterpart of an effective Hamiltonian for a strongly trimerized kagome lattice. Although the Hamiltonian only has a discrete symmetry, the classical groundstate manifold has a continuous global rotational symmetry. Two cases should be distinguished for the sign of the exchange constant. In one case, the groundstate has a 120^\circ spin structure. To determine the transition temperature, we perform Monte-Carlo simulations and measure specific heat, the order parameter as well as the associated Binder cumulant. In the other case, the classical groundstates are macroscopically degenerate. A thermal order-by-disorder mechanism is predicted to select another 120^\circ spin-structure. A finite but very small transition temperature is detected by Monte-Carlo simulations using the exchange method.Comment: 11 pages including 9 figures, uses IOP style files; to appear in J. Phys.: Condensed Matter (proceedings of HFM2006

Multicanonical Study of the 3D Ising Spin Glass

We simulated the Edwards-Anderson Ising spin glass model in three dimensions via the recently proposed multicanonical ensemble. Physical quantities such as energy density, specific heat and entropy are evaluated at all temperatures. We studied their finite size scaling, as well as the zero temperature limit to explore the ground state properties.Comment: FSU-SCRI-92-121; 7 pages; sorry, no figures include

State Hierarchy Induced by Correlated Spin Domains in short range spin glasses

We generate equilibrium configurations for the three and four dimensional Ising spin glass with Gaussian distributed couplings at temperatures well below the transition temperature T_c. These states are analyzed by a recently proposed method using clustering. The analysis reveals a hierarchical state space structure. At each level of the hierarchy states are labeled by the orientations of a set of correlated macroscopic spin domains. Our picture of the low temperature phase of short range spin glasses is that of a State Hierarchy Induced by Correlated Spin domains (SHICS). The complexity of the low temperature phase is manifest in the fact that the composition of such a spin domain (i.e. its constituent spins), as well as its identifying label, are defined and determined by the ``location'' in the state hierarchy at which it appears. Mapping out the phase space structure by means of the orientations assumed by these domains enhances our ability to investigate the overlap distribution, which we find to be non-trivial. Evidence is also presented that these states may have a non-ultrametric structure.Comment: 30 pages, 17 figure

Critical Behavior of the Three-Dimensional Ising Spin Glass

We have simulated, using parallel tempering, the three dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (L=20) has been studied using a dedicated computer (the SUE machine). We have obtained, measuring the correlation length in the critical region, a strong evidence for a second-order finite temperature phase transition ruling out other possible scenarios like a Kosterlitz-Thouless phase transition. Precise values for the $\nu$ and $\eta$ critical exponents are also presented.Comment: RevTex; 12 pages plus 5 ps figures. Final version to be published in PR

Using network-flow techniques to solve an optimization problem from surface-physics

The solid-on-solid model provides a commonly used framework for the description of surfaces. In the last years it has been extended in order to investigate the effect of defects in the bulk on the roughness of the surface. The determination of the ground state of this model leads to a combinatorial problem, which is reduced to an uncapacitated, convex minimum-circulation problem. We will show that the successive shortest path algorithm solves the problem in polynomial time.Comment: 8 Pages LaTeX, using Elsevier preprint style (macros included