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Search Results: 1 - 10 of 495 matches for " Pierluigi Contucci "
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Stochastic Stability: a Review and Some Perspectives
Pierluigi Contucci
Physics , 2009, DOI: 10.1007/s10955-009-9887-x
Abstract: A review of the stochastic stability property for the Gaussian spin glass models is presented and some perspectives discussed.
Replica equivalence in the Edwards-Anderson model
Pierluigi Contucci
Physics , 2003, DOI: 10.1088/0305-4470/36/43/020
Abstract: After introducing and discussing the "link-overlap" between spin configurations we show that the Edwards-Anderson model has a "replica-equivalent" quenched equilibrium state, a property introduced by Parisi in the description of the mean-field spin-glass phase which generalizes ultrametricity. Our argument is based on the control of fluctuations through the property of stochastic stability and works for all the finite-dimensional spin-glass models.
Stochastic Stability and the Spin Glass Phase. The State of the Art for Mean Field and Finite Dimensional Models
Pierluigi Contucci
Physics , 2012,
Abstract: Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorisation rules for the overlap distribution. A comparison between the state of the art for mean field and finite dimensional models is shortly discussed.
Toward a Classification of Stochastically Stable Quenched Measures
Pierluigi Contucci
Mathematics , 2002,
Abstract: In this short note we study the fourth order consequences of the stochastic stability property for mean field spin glass models introduced in previous paper by Aizenman and Contucci. We show that due to a remarkable cancellation mechanism it reduces to the well known second order version as predicted by Parisi's replica-equivalent ansatz.
Correlation Inequalities for Spin Glass in one Dimension
Pierluigi Contucci,Francesco Unguendoli
Physics , 2007,
Abstract: We prove two inequalities for the direct and truncated correlation for the nearest-neighboor one-dimensional Edwards-Anderson model with symmetric quenched disorder. The second inequality has the opposite sign of the GKS inequality of type II. In the non symmetric case with positive average we show that while the direct correlation keeps its sign the truncated one changes sign when crossing a suitable line in the parameter space. That line separates the regions satisfying the GKS second inequality and the one proved here.
Bipartite Mean Field Spin Systems. Existence and Solution
Ignacio Gallo,Pierluigi Contucci
Physics , 2007,
Abstract: A mean field spin system consisting two interacting groups each with homogeneous interaction coefficients is introduced and studied. Existence of the thermodynamic limit is shown by an asymptotic sub-addittivity method and factorization of correlation functions is proved almost everywhere. The free energy solution of the model is obtained by upper and lower bounds and by showing that their difference vanishes for large volumes.
Thermodynamic Limit for Spin Glasses. Beyond the Annealed Bound
Pierluigi Contucci,Shannon Starr
Physics , 2008, DOI: 10.1007/s10955-008-9676-y
Abstract: Using a correlation inequality of Contucci and Lebowitz for spin glasses, we demonstrate existence of the thermodynamic limit for short-ranged spin glasses, under weaker hypotheses than previously available, namely without the assumption of the annealed bound.
Correlation Inequalities for Spin Glasses
Pierluigi Contucci,Joel Lebowitz
Physics , 2006, DOI: 10.1007/s00023-007-0342-8
Abstract: We prove a correlation type inequality for spin systems with quenched symmetric random interactions. This gives monotonicity of the pressure with respect to the strength of the interaction for a class of spin glass models. Consequences include existence of the thermodynamic limit for the pressure and bounds on the surface pressure. We also describe other conjectured inequalities for such systems.
Monotonicity and Thermodynamic Limit for Short Range Disordered Models
Pierluigi Contucci,Sandro Graffi
Physics , 2003, DOI: 10.1023/B:JOSS.0000019812.03696.b7
Abstract: If the variance of a short range Gaussian random potential grows like the volume its quenched thermodynamic limit is reached monotonically.
Modeling Society with Statistical Mechanics: an Application to Cultural Contact and Immigration
Pierluigi Contucci,Stefano Ghirlanda
Physics , 2006,
Abstract: We introduce a general modeling framework to predict the outcomes, at the population level, of individual psychology and behavior. The framework prescribes that researchers build a cost function that embodies knowledge of what trait values (opinions, behaviors, etc.) are favored by individual interactions under given social conditions. Predictions at the population level are then drawn using methods from statistical mechanics, a branch of theoretical physics born to link the microscopic and macroscopic behavior of physical systems. We demonstrate our approach building a model of cultural contact between two cultures (e.g., immigration), showing that it is possible to make predictions about how contact changes the two cultures.
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