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Sep 23, 2013
09/13

by
P. Contucci; C. Giardina'

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We prove the property of stochastic stability previously introduced as a consequence of the (unproved) continuity hypothesis in the temperature of the spin-glass quenched state. We show that stochastic stability holds in beta-average for both the Sherrington-Kirkpatrick model in terms of the square of the overlap function and for the Edwards-Anderson model in terms of the bond overlap. We show that the volume rate at which the property is reached in the thermodynamic limit is V^{-1}. As a...

Source: http://arxiv.org/abs/math-ph/0408002v2

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Sep 18, 2013
09/13

by
C. Giardina'; J. Kurchan

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We introduce a family of Hamiltonian models for heat conduction with and without momentum conservation. They are analytically solvable in the high temperature limit and can also be efficiently simulated. In all cases Fourier law is verified in one dimension.

Source: http://arxiv.org/abs/cond-mat/0502485v2

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Sep 19, 2013
09/13

by
C. Giardina'; R. Livi

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The problem of the existence of a Strong Stochasticity Threshold in the FPU-beta model is reconsidered, using suitable microcanonical observables of thermodynamic nature, like the temperature and the specific heat. Explicit expressions for these observables are obtained by exploiting rigorous methods of differential geometry. Measurements of the corresponding temporal autocorrelation functions locate the threshold at a finite value of the energy density, that results to be indipendent of the...

Source: http://arxiv.org/abs/chao-dyn/9709015v1

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Sep 18, 2013
09/13

by
P. Contucci; C. Giardina'

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We comment on recent numerical experiments by G.Hed and E.Domany [cond-mat/0608535v2] on the quenched equilibrium state of the Edwards-Anderson spin glass model. The rigorous proof of overlap identities related to replica equivalence shows that the observed violations of those identities on finite size systems must vanish in the thermodynamic limit. See also the successive version cond-mat/0608535v4

Source: http://arxiv.org/abs/cond-mat/0611138v2

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Sep 22, 2013
09/13

by
C. Giardina; F. Redig; K. Vafayi

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We prove a comparison inequality between a system of independent random walkers and a system of random walkers which either interact by attracting each other -- a process which we call here the symmetric inclusion process (SIP) -- or repel each other -- a generalized version of the well-known symmetric exclusion process. As an application, new correlation inequalities are obtained for the SIP, as well as for some interacting diffusions which are used as models of heat conduction, -- the...

Source: http://arxiv.org/abs/0906.4664v3

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Sep 19, 2013
09/13

by
P. Collet; C. Giardina; F. Redig

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We consider matching with shifts for Gibbsian sequences. We prove that the maximal overlap behaves as $c\log n$, where $c$ is explicitly identified in terms of the thermodynamic quantities (pressure) of the underlying potential. Our approach is based on the analysis of the first and second moment of the number of overlaps of a given size. We treat both the case of equal sequences (and nonzero shifts) and independent sequences.

Source: http://arxiv.org/abs/0708.2165v3

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Sep 21, 2013
09/13

by
A. Bianchi; P. Contucci; C. Giardina'

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If the Boltzmann-Gibbs state $\omega_N$ of a mean-field $N$-particle system with Hamiltonian $H_N$ verifies the condition $$ \omega_N(H_N) \ge \omega_N(H_{N_1}+H_{N_2}) $$ for every decomposition $N_1+N_2=N$, then its free energy density increases with $N$. We prove such a condition for a wide class of spin models which includes the Curie-Weiss model, its p-spin generalizations (for both even and odd p), its random field version and also the finite pattern Hopfield model. For all these cases...

Source: http://arxiv.org/abs/math-ph/0311017v2

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Sep 18, 2013
09/13

by
P. Contucci; C. Giardina'; J. Pule'

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We provide a very simple proof for the existence of the thermodynamic limit for the quenched specific pressure for classical and quantum disordered systems on a $d$-dimensional lattice, including spin glasses. We develop a method which relies simply on Jensen's inequality and which works for any disorder distribution with the only condition (stability) that the quenched specific pressure is bounded.

Source: http://arxiv.org/abs/cond-mat/0401211v4

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Sep 20, 2013
09/13

by
C. Giardiná; J. Kurchan; F. Redig

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We study a model of heat conduction with stochastic diffusion of energy. We obtain a dual particle process which describes the evolution of all the correlation functions. An exact expression for the covariance of the energy exhibits long-range correlations in the presence of a current. We discuss the formal connection of this model with the simple symmetric exclusion process.

Source: http://arxiv.org/abs/cond-mat/0612198v1

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Sep 17, 2013
09/13

by
M. Degli Esposti; C. Giardina'; S. Graffi

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The Random Orthogonal Model (ROM) of Marinari-Parisi-Ritort [MPR1,MPR2] is a model of statistical mechanics where the couplings among the spins are defined by a matrix chosen randomly within the orthogonal ensemble. It reproduces the most relevant properties of the Parisi solution of the Sherrington-Kirckpatrick model. Here we compute the energy distribution, and work out an extimate for the two-point correlation function. Moreover, we show exponential increase of the number of metastable...

Source: http://arxiv.org/abs/cond-mat/0207681v1

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Sep 18, 2013
09/13

by
C. Giardina'; N. V. Priezjev; J. M. Kosterlitz

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The three dimensional XY model with quenched random disorder and finite screening is studied. We argue that the system scales to model with $\lambda\simeq 0\simeq T$ and the resulting effective model is studied numerically by defect energy scaling. In zero external field we find that there exists a true superconducting phase with a stiffness exponent $\theta\simeq +1.0$ for weak disorder. For low magnetic field and weak disorder, there is also a superconducting phase with $\theta\simeq +1.0$...

Source: http://arxiv.org/abs/cond-mat/0202487v2

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Jul 20, 2013
07/13

by
C. Giardina'; R. Livi; A. Politi; M. Vassalli

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We discuss the thermal conductivity of a chain of coupled rotators, showing that it is the first example of a 1d nonlinear lattice exhibiting normal transport properties in the absence of an on-site potential. Numerical estimates obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the...

Source: http://arxiv.org/abs/chao-dyn/9910023v1

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Sep 18, 2013
09/13

by
M. Degli Esposti; C. Giardina'; S. Graffi; S. Isola

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We consider the zero-temperature dynamics for the infinite-range, non translation invariant one-dimensional spin model introduced by Marinari, Parisi and Ritort to generate glassy behaviour out of a deterministic interaction. It is shown that there can be a large number of metatastable (i.e., one-flip stable) states with very small overlap with the ground state but very close in energy to it, and that their total number increases exponentially with the size of the system.

Source: http://arxiv.org/abs/cond-mat/0006476v1

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Sep 19, 2013
09/13

by
P. Contucci; M. Degli Esposti; C. Giardina; S. Graffi

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Let $\{E_{\s}(N)\}_{\s\in\Sigma_N}$ be a family of $|\Sigma_N|=2^N$ centered unit Gaussian random variables defined by the covariance matrix $C_N$ of elements $\displaystyle c_N(\s,\tau):=\av{E_{\s}(N)E_{\tau}(N)}$, and $H_N(\s) = - \sqrt{N} E_{\s}(N)$ the corresponding random Hamiltonian. Then the quenched thermodynamical limit exists if, for every decomposition $N=N_1+N_2$, and all pairs $(\s,\t)\in \Sigma_N\times \Sigma_N$: $$ c_N(\s,\tau)\leq \frac{N_1}{N} c_{N_1}(\pi_1(\s),\pi_1(\tau))+...

Source: http://arxiv.org/abs/math-ph/0206007v2

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Sep 23, 2013
09/13

by
G. Carinci; J. -R. Chazottes; C. Giardina; F. Redig

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We study the so-called nonconventional averages in the context of lattice spin systems, or equivalently random colourings of the integers. For i.i.d. colourings, we prove a large deviation principle for the number of monochromatic arithmetic progressions of size two in the box $[1,N]\cap \N$, as $N\to\infty$, with an explicit rate function related to the one-dimensional Ising model. For more general colourings, we prove some bounds for the number of monochromatic arithmetic progressions of...

Source: http://arxiv.org/abs/1110.2354v3

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Sep 18, 2013
09/13

by
L. Bussolari; P. Contucci; M. Degli Esposti; C. Giardina'

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We perform a statistical analysis of deterministic energy-decreasing algorithms on mean-field spin models with complex energy landscape like the Sine model and the Sherrington Kirkpatrick model. We specifically address the following question: in the search of low energy configurations is it convenient (and in which sense) a quick decrease along the gradient (greedy dynamics) or a slow decrease close to the level curves (reluctant dynamics)? Average time and wideness of the attraction basins are...

Source: http://arxiv.org/abs/cond-mat/0210545v2

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Sep 22, 2013
09/13

by
P. Contucci; C. Giardina'; C. Giberti; F. Unguendoli; C. Vernia

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In a standard NP-complete optimization problem we introduce an interpolating algorithm between the quick decrease along the gradient (greedy dynamics) and a slow decrease close to the level curves (reluctant dynamics). We find that for a fixed elapsed computer time the best performance of the optimization is reached at a special value of the interpolation parameter, considerably improving the results of the pure cases greedy and reluctant.

Source: http://arxiv.org/abs/math-ph/0309063v1

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Sep 20, 2013
09/13

by
P. Contucci; C. Giardina'; C. Giberti; G. Parisi; C. Vernia

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We test the property of ultrametricity for the spin glass three-dimensional Edwards-Anderson model in zero magnetic field with numerical simulations up to $20^3$ spins. We find an excellent agreement with the prediction of the mean field theory. Since ultrametricity is not compatible with a trivial structure of the overlap distribution our result contradicts the droplet theory.

Source: http://arxiv.org/abs/cond-mat/0607376v4

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Sep 22, 2013
09/13

by
L. Bussolari; P. Contucci; C. Giardina'; C. Giberti; F. Unguendoli; C. Vernia

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We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein conformation, image restoration. We show the performances of two algorithms, the``greedy'' (quick decrease along the gradient) and the``reluctant'' (slow decrease close to the level curves) as well as those of a``stochastic convex interpolation''of the two....

Source: http://arxiv.org/abs/math/0309058v1