1,721,011 research outputs found
Comment on ``Both site and link overlap distributions are non trivial in 3-dimensional Ising spin glasses'', cond-mat/0608535v2
No full textWe 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/0608535v
Factorization properties in the three-dimensional Edwards-Anderson model
Full text linkWe study the three-dimensional Gaussian Edwards-Anderson model and find numerical evidence of a simple factorization law of the link-overlaps distributions at large volumes. We also perform the same analysis for the standard overlap for which instead the lack of factorization persists, increasing the size of the system. Our results open new perspectives in the study of the two different overlaps emphasizing the importance of the concept of factorization-triviality to distiniguish their role. © 2005 The American Physical Society
Lack of monotonicity in spin glass correlation functions
No full textWe study the response of a spin glass system with respect to the rescaling of its interaction random variables and investigate numerically the behaviour of the correlation functions with respect to the volume. While for a ferromagnet the local energy correlation functions increase monotonically with the scale and, by consequence, with respect to the volume of the system we find that in a general spin glass model those monotonicities are violated
Toward a quantitative approach to migrants integration
No full textMigration phenomena and all the related issues, like integration of different social groups, are intrinsically complex problems since they strongly depend on several competitive mechanisms as economic factors, cultural differences and many others. By identifying a few essential assumptions, and using the statistical mechanics of complex systems, we propose a novel quantitative approach that provides a minimal theory for those phenomena. We show that the competitive interactions in decision making between a population of N host citizens and P immigrants, a bi-partite spin-glass, give rise to a social consciousness inside the host community in the sense of the associative memory of neural networks. The theory leads to a natural quantitative definition of migrant's “integration" inside the community. From the technical point of view this minimal picture assumes, as control parameters, only general notions like the strength of the random interactions, the ratio between the sizes of the two parties and the cultural influence. Few steps forward, toward more refined models, which include a digression on the kind of the felt experiences and some structure on the random interaction topology (as dilution to avoid the plain mean-field approach) and correlations of experiences felt between the two parties (biasing the distribution of the coupling) are discussed at the end, where we show the robustness of our approach
Correlation Inequalities for Spin Glass in one Dimension
No full textWe prove two inequalities for the direct and truncated correlation for the nearest-neighboor one-dimensional Edwards-Anderson model with symmetric quenched dis-order. The second inequality has the opposite sign of the GKS inequality of typeII. In the non symmetric case with positive average we show that while the directcorrelation keeps its sign the truncated one changes sign when crossing a suitableline in the parameter space. That line separates the regions satisfying the GKSsecond inequality and the one proved here
Low energy excitations of vector spin glasses
Full text linkIl lavoro contenuto in questa tesi riguarda il problema dell'eccitazioni di bassa energia dei modelli di vetri di spin vettoriali. Viene proposto uno studio analitico e numerico di tre modelli: il primo consiste in un vetro di spin di Heisenberg con campo magnetico esterno random con grafo di interazioni denso, il secondo in un modello p spin di Heisenberg con grafo di interazioni denso, il terzo infine in un modello di Heisenberg con campo magnetico esterno random e grafo di interazioni diluito.
Questi modelli sono valutati rispetto al comportamento dell'eccitazioni dei sistemi vetrosi a basse temperature: in particolare, nella tesi si mostra che questi modelli posseggono delle fasi in cui la densità degli stati è senza gap e i modi sono quasi localizzati. Nel modello sparso la densità degli stati ha una dipendenza quartica dalla frequenza, in accordo con molteplici misure di questa quantità reperibili dalla letteratura sui modelli vetrosi computazionali. In tutti e tre i casi di studio, la transizione nella fase del vetro di spin è caratterizzata rispetto al comportamento dei modi soffici. Troviamo che nei modelli densi la transizione del vetro di spin è una transizione di delocalizzazione dei modi soffici. Nel caso sparso, la delocalizzazione alla transizione si manifesta in forma più debole. Questi risultati ampliano la nostra comprensione del punto critico di temperatura nulla, mostrando come l'emergenza di un ordinamento da vetro di spin modifichi la risposta del sistema a piccole perturbazioni magnetiche.The work of this thesis concerns the problem of linear low energy excitations of vector spin glass models. An analytical and numerical study is carried out, considering a fully connected random-field Heisenberg model at zero temperature, a fully-connected vector p-spin glass model and a sparse random-field Heisenberg model. We test these models against the low temperature behavior of finite dimensional glassy systems, in particular we show that they posses phases where the density of states is gapless with quasi-localised modes. In the case of the sparse model, we show that the density of states follows a quartic law at low frequency, consistently with several recent measures of this quantity that can be found in the literature of computer glasses. In all the three models, the spin glass transition is characterised in terms of the behavior of the softest excitations. We found that in the fully connected models the zero temperature spin glass transition in a field is a delocalisation transition of the softest modes. In the sparse case, a weaker form of delocalisation appears at the transition. These results broaden our understanding of the zero temperature critical point, by showing how spin glass ordering affects the way the system responds to small magnetic perturbations.Le travail de cette thèse concerne le problème des excitations linéaires à basse énergie des modèles de verre de spin vectoriel. Une étude analytique et numérique est menée, considérant un modèle de Heisenberg à champ aléatoire entièrement connecté à température nulle, un modèle de verre de spin p vectoriel entièrement connecté et un modèle de Heisenberg dilué à champ aléatoire. Nous testons ces modèles par rapport au comportement à basse température des systèmes vitreux de dimension finie, en particulier nous montrons qu'ils possèdent des phases où la densité d'états est sans lacunes avec des modes quasi localisés. Dans le cas du modèle dilué, nous montrons que la densité d'états suit une loi quartique à basse fréquence, en accord avec plusieurs mesures récentes de cette quantité que l'on peut trouver dans la littérature des modèles computationnels de verres. Dans les trois modèles, la transition de verre de spin est caractérisée en termes de comportement des excitations les plus douces. Nous avons constaté que dans les modèles entièrement connectés, la transition de verre de spin à température zéro dans un champ est une transition de délocalisation des modes les plus douces. Dans le cas dilué, une forme plus faible de délocalisation apparaît à la transition. Ces résultats élargissent notre compréhension du point critique à température zéro, en montrant comment l'ordre du verre de spin affecte la façon dont le système répond à de petites perturbations magnétiques
Modelling Complex Systems with Statistical Mechanics: The Computational Approach
No full textReal-world phenomena are often described by complex systems with competitive and cooperative behaviour. Such systems, as much as the described phenomena, are hard to understand in a scientific perspective mainly due to the lack of general exact solutions. For cases like this, the computational sciences provide a very useful virtual laboratory. The case of disordered systems is an example of scientific computing techniques being used to test theoretical predictions and uncover new phenomena that remain unreachable by traditional analytical methods
A diffusive strategic dynamics for social systems
No full textWe propose a model for the dynamics of a social system, which includes diffusive effects and a biased rule for spin-flips, reproducing the effect of strategic choices. This model is able to mimic some phenomena taking place during marketing or political campaigns. Using a cost function based on the Ising model defined on the typical quenched interaction environments for social systems (Erdös-Renyi graph, small-world and scale-free networks), we find, by numerical simulations, that a stable stationary state is reached, and we compare the final state to the one obtained with standard dynamics, by means of total magnetization and magnetic susceptibility. Our results show that the diffusive strategic dynamics features a critical interaction parameter strictly lower than the standard one. We discuss the relevance of our findings in social systems
Introduction to Special Issue: Statistical Mechanics on Random Structures
Full text linkIntroduction to Special Issue: Statistical Mechanics on Random Structure
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