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Enzo Marinari

Publications and source records attributed to Enzo Marinari.

At least 73 records · Page 4Linked to original sources
arXiv2003

Scalings of domain wall energies in two dimensional Ising spin glasses

We study domain wall energies of two dimensional spin glasses. The scaling of these energies depends on the model's distribution of quenched random couplings, falling into three different classes. The first class is associated with the exponent theta =-0.28, the other two classes have theta = 0, as can be justified theoretically. In contrast to previous claims, we find that theta=0 does not indicate d=d_l but rather d <= d_l, where d_l is the lower critical dimension.

cond-mat.dis-nn↗
arXiv2003

On the Tail of the Overlap Probability Distribution in the Sherrington--Kirkpatrick Model

We investigate the large deviation behavior of the overlap probability density in the Sherrington--Kirkpatrick model from several analytical perspectives. First we analyze the spin glass phase using the coupled replica scheme. Here generically $\frac1N \log P_N(q)$ $\approx$ $- {\cal A}$ $((|q|-q_{EA})^3$, and we compute the first correction to the expansion of $\A$ in powers of $T_c-T$. We study also the $q=1$ case, where $P(q)$ is know exactly. Finally we study the paramagnetic phase, where exact results valid for all $q$'s are obtained. The overall agreement between the various points of view is very satisfactory. Data from large scale numerical simulations show that the predicted behavior can be detected already on moderate lattice sizes.

cond-mat.stat-mech↗
arXiv2003

A Quantitative Clustering Approach to Ultrametricity in Spin Glasses

We discuss the problem of ultrametricity in mean field spin glasses by means of a hierarchical clustering algorithm. We complement the clustering approach with quantitative testing: we discuss both in some detail. We show that the elimination of the (in this context accidental) spin flip symmetry plays a crucial role in the analysis, since the symmetry hides the real nature of the data. We are able to use in the analysis disorder averaged quantities. We are able to exhibit a number of features of the low $T$ phase of the mean field theory, and to claim that the full hierarchical structure can be observed without ambiguities only on very large lattice volumes, not currently accessible by numerical simulations.

cond-mat.stat-mech↗
arXiv2003

Localization of Denaturation Bubbles in Random DNA Sequences

We study the thermodynamic and dynamic behaviors of twist-induced denaturation bubbles in a long, stretched random sequence of DNA. The small bubbles associated with weak twist are delocalized. Above a threshold torque, the bubbles of several tens of bases or larger become preferentially localized to \AT-rich segments. In the localized regime, the bubbles exhibit ``aging'' and move around sub-diffusively with continuously varying dynamic exponents. These properties are derived using results of large-deviation theory together with scaling arguments, and are verified by Monte-Carlo simulations.

cond-mat.stat-mech↗
arXiv2002

Overlap Among States at Different Temperatures in the SK Model

We discuss the issue of temperature chaos in the Sherrington--Kirkpatrick spin glass mean field model. We numerically compute probability distributions of the overlap among (equilibrium) configurations at two different values of the temperature, both in the spin glass phase. The situation on our medium size systems is clearly non-chaotic, but a weak form of chaos could be emerging on very large lattices.

cond-mat.dis-nn↗
arXiv2001

Zero Temperature Properties of RNA Secondary Structures

We analyze different microscopic RNA models at zero temperature. We discuss both the most simple model, that suffers a large degeneracy of the ground state, and models in which the degeneracy has been remove, in a more or less severe manner. We calculate low-energy density of states using a coupling perturbing method, where the ground state of a modified Hamiltonian, that repels the original ground state, is determined. We evaluate scaling exponents starting from measurements of overlaps and energy differences. In the case of models without accidental degeneracy of the ground state we are able to clearly establish the existence of a glassy phase with $θ\simeq 1/3$.

cond-mat.dis-nn↗
arXiv2001

Correlation Time Scales in the Sherrington-Kirkpatrick Model

We investigate the dynamical behavior of the Sherrington-Kirkpatrick mean field model of spin glasses by numerical simulation. All the time scales tau we have measured behave like ln(tau) propto N^epsilon, where N is the number of spins and epsilon \simeq 1/3. This is true whether the autocorrelation function used to define tau is sensitive to the full reversal of the system or not.

cond-mat.stat-mech↗
arXiv2000

On the Effects of Changing the Boundary Conditions on the Ground State of Ising Spin Glasses

We compute and analyze couples of ground states of 3D spin glass systems with the same quenched noise but periodic and anti-periodic boundary conditions for different lattice sizes. We discuss the possible different behaviors of the system, we analyze the average link overlap, the probability distribution of window overlaps (among ground states computed with different boundary conditions) and the spatial overlap and link overlap correlation functions. We establish that the picture based on Replica Symmetry Breaking correctly describes the behavior of 3D Spin Glasses.

cond-mat.dis-nn↗
arXiv2000

On the Energy Minima of the SK Model

We study properties of the energy minima obtained by quenching equilibrium configurations of the Sherrington-Kirkpatrick (SK) mean field spin glass. We measure the probability distribution of the overlap among quenched configurations and the quenched energy, looking at the dependence on the starting equilibrium temperature, and performing a systematic analysis of finite size effects.

cond-mat.dis-nn↗
arXiv1999

Comment on "Numerical Study on Aging Dynamics in the 3D Ising Spin Glass Model"

We show that the dynamical behavior of the 3D Ising spin glass with Gaussian couplings is not compatible with a droplet dynamics. We show that this is implied from the data of reference cond-mat/9904143, that, when analyzed in an accurate way, give multiple evidences of this fact. Our study is based on the analysis of the overlap-overlap correlation function, at different values of the separation r and of the time t.

cond-mat.stat-mech↗
arXiv1998

Critical Behavior of the 4D Spin Glass in Magnetic Field

We present numerical simulations of the 4D Edwards Anderson Ising spin glass with binary couplings. Our results, in the midst of strong finite size effects, suggest the existence of a spin glass phase transition. We present a preliminar determination of critical exponents. We discuss spin glass susceptibilities, cumulants of the overlap and energy overlap probability distributions, finite size effects, and the behavior of the disorder dependent and of the integrated probability distribution.

cond-mat.dis-nn↗
arXiv1998

Mean-field behavior of the sandpile model below the upper critical dimension

We present results of large scale numerical simulations of the Bak, Tang and Wiesenfeld sandpile model. We analyze the critical behavior of the model in Euclidean dimensions $2\leq d\leq 6$. We consider a dissipative generalization of the model and study the avalanche size and duration distributions for different values of the lattice size and dissipation. We find that the scaling exponents in $d=4$ significantly differ from mean-field predictions, thus suggesting an upper critical dimension $d_c\geq 5$. Using the relations among the dissipation rate $ε$ and the finite lattice size $L$, we find that a subset of the exponents displays mean-field values below the upper critical dimensions. This behavior is explained in terms of conservation laws.

cond-mat.stat-mech↗
arXiv1997

Energy constrained sandpile models

We study two driven dynamical systems with conserved energy. The two automata contain the basic dynamical rules of the Bak, Tang and Wiesenfeld sandpile model. In addition a global constraint on the energy contained in the lattice is imposed. In the limit of an infinitely slow driving of the system, the conserved energy $E$ becomes the only parameter governing the dynamical behavior of the system. Both models show scale free behavior at a critical value $E_c$ of the fixed energy. The scaling with respect to the relevant scaling field points out that the developing of critical correlations is in a different universality class than self-organized critical sandpiles. Despite this difference, the activity (avalanche) probability distributions appear to coincide with the one of the standard self-organized critical sandpile.

cond-mat.stat-mech↗
arXiv1997

Off-Equilibrium Dynamics of a 4D Spin Glass with Asymmetric Couplings

We study the off-equilibrium dynamics of the Edwards-Anderson spin glass in four dimensions under the influence of a non-hamiltonian perturbation. We find that for small asymmetry the model behaves as the hamiltonian one, while for large asymmetry the behaviour of the model can be well described by an interrupted aging scenario. The autocorrelation function C(t_w+τ,t_w) scales as τ/t_w^β, with βa function of the asymmetry. For very long waiting times the previous regime crosses over to a time translational invariant regime (TTI) with stretched exponential relaxation. The model does not show signs of reaching a TTI regime for weak asymmetry, but in the aging regime the exponent βis always different from one, showing a non trivial aging scenario.

cond-mat.dis-nn↗
arXiv1997

Numerical Simulations of the Dynamical Behavior of the SK Model

We study the dynamical behavior of the Sherrington Kirkpatrick model. Thanks to the APE supercomputer we are able to analyze large lattice volumes, and to investigate the low $T$ region. We present a determination of the remnant magnetization and of its time decay exponent, of the energy time decay exponent, and we discuss aging phenomena in the model.

cond-mat.dis-nn↗
arXiv1997

Violation of the Fluctuation Dissipation Theorem in Finite Dimensional Spin Glasses

We study the violation of the fluctuation-dissipation theorem in the three and four dimensional Gaussian Ising spin glasses using on and off equilibrium simulations. We have characterized numerically the function X(C) that determine the violation and we have studied its scaling properties. Moreover we have computed the function x(C) which characterize the breaking of the replica symmetry directly from equilibrium simulations. The two functions are numerically equal and in this way we have established that the conjectured connection between the violation of fluctuation dissipation theorem in the off-equilibrium dynamics and the replica symmetry breaking at equilibrium holds for finite dimensional spin glasses. These results point to a spin glass phase with spontaneously broken replica symmetry in finite dimensional spin glasses.

cond-mat.dis-nn↗
arXiv1997

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.

cond-mat.dis-nn↗