arXiv subjects

Pierluigi Contucci

Publications and source records attributed to Pierluigi Contucci.

At least 73 records · Page 4Linked to original sources

arXiv2009

On the structure of correlations in the three dimensional spin glasses

We investigate the low temperature phase of three-dimensional Edwards-Anderson model with Bernoulli random couplings. We show that at a fixed value $Q$ of the overlap the model fulfills the clustering property: the connected correlation functions between two local overlaps decay as a power whose exponent is independent of $Q$ for all $0\le |Q| < q_{EA}$. Our findings are in agreement with the RSB theory and show that the overlap is a good order parameter.

cond-mat.dis-nn↗

arXiv2008

Parameter Evaluation of a Simple Mean-Field Model of Social Interaction

The aim of this work is to implement a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. A class of simple mean field discrete models is introduced and discussed both from the theoretical and phenomenological point of view. We propose a parameter evaluation procedure and test it by fitting our model against three families of data coming from different cases: the estimated interaction parameters are found to have similar positive values establishing a quantitative confirmation of the peer imitation behavior found in social psychology. Moreover all the values of the interaction parameters belong to the phase transition regime suggesting its possible role in the study of social systems.

physics.soc-ph↗

arXiv2008

Thermodynamic Limit for Spin Glasses. Beyond the Annealed Bound

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.

math-ph↗

arXiv2008

Tackling climate change through energy efficiency: mathematical models for evidence-based public policy recommendations

Promoting and increasing energy efficiency is a promising method of reducing CO2 emissions and avoiding the potentially devastating effects of climate change. The question is: How do we induce a cultural or behavioural change whereby people nationally and globally adopt more energy efficient lifestyles? We propose a new family of mathematical models, based on a statistical mechanics extension of discrete choice theory, that offer a set of formal tools to systematically analyse and quantify this problem. An application example could be to predict the percentage of people choosing to buy new energy efficient light bulbs instead of the traditional incandescent versions. Through statistical evaluation of survey responses, the models can identify the key driving factors in the decision-making process; for example, the extent to which people imitate each other. These models allow us to incorporate the effect of social interactions could help us identify 'tipping points' at a societal level. This knowledge could be used to trigger structural changes in our society. The results may provide tangible and deliverable evidence-based policy options to decision-makers. We believe that these models offer an opportunity for the research community-in both the social and physical sciences-and decision-makers in the private and public sectors to work together towards preventing the potentially devastating social, economic and environmental effects of climate change.

physics.soc-ph↗

arXiv2008

Spin Glass Identities and the Nishimori Line

For a general spin glass model with asymmetric couplings we prove a family of identities involving expectations of generalized overlaps and magnetizations in the quenched state. Those identities holds pointwise in the Nishimori line and are reached at the rate of the inverse volume while, in the general case, they can be proved in integral average.

cond-mat.dis-nn↗

arXiv2008

Equilibria of culture contact derived from ingroup and outgroup attitudes

Modern societies feature an increasing contact between cultures, yet we have a poor understanding of what the outcomes might be. Here we consider a mathematical model of contact between social groups, grounded in social psychology and analyzed using tools from statistical physics. We use the model to study how a culture might be affected by immigration. We find that in some cases residents' culture is relatively unchanged, but in other cases residents may adopt the opinions and beliefs of immigrants. The decisive factors are each group's cultural legacy and its attitudes towards in- and out-groups. The model can also predict how social policies may influence the outcome of culture contact.

physics.soc-ph↗

arXiv2008

Lack of monotonicity in spin glass correlation functions

We 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.

cond-mat.dis-nn↗

arXiv2008

Correlation Inequalities for Spin Glass in one Dimension

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.

math-ph↗

arXiv2007

Bipartite Mean Field Spin Systems. Existence and Solution

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.

cond-mat.stat-mech↗

arXiv2007

Comment on "Ultrametricity in the Edwards-Anderson Model"

In a recent interesting Letter Contucci {\it et al.} have investigated several properties of the three-dimensional (3d) Edwards-Anderson (EA) Ising spin glass. They claim to have found strong numerical evidence for the presence of a complex ultrametric structure similar to the one described by the replica symmetry breaking solution of the mean field model. We illustrate by numerical simulations that the relations used by Contucci {\it et al.} as evidence for an ultrametric structure in the 3d EA model are fulfilled to similar accuracy in the two-dimensional EA model, which is well-described by the droplet picture and has no spin glass phase at finite temperature. We conclude that the data presented in the Contucci {\it et al.} Letter is not sufficient to dismiss the possibility that, e.g., the droplet model might describe the behavior of the 3d EA model.

cond-mat.dis-nn↗

arXiv2007

Phase transitions in social sciences: two-populations mean field theory

A new mean field statistical mechanics model of two interacting groups of spins is introduced and the phase transition studied in terms of their relative size. A jump of the average magnetization is found for large values of the mutual interaction when the relative percentage of the two populations crosses a critical threshold. It is shown how the critical percentage depends on internal interactions and on the initial magnetizations. The model is interpreted as a prototype of resident-immigrant cultural interaction and conclusions from the social sciences perspectives are drawn.

physics.soc-ph↗

arXiv2006

Correlation Inequalities for Spin Glasses

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.

cond-mat.dis-nn↗

arXiv2006

Modeling Society with Statistical Mechanics: an Application to Cultural Contact and Immigration

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.

physics.soc-ph↗

arXiv2006

Overlap Equivalence in the Edwards-Anderson Model

We study the relative fluctuations of the link overlap and the square standard overlap in the three dimensional Gaussian Edwards-Anderson model with zero external field. We first analyze the correlation coefficient and find that the two quantities are uncorrelated above the critical temperature. Below the critical temperature we find that the link overlap has vanishing fluctuations for fixed values of the square standard overlap and large volumes. Our data show that the conditional variance scales to zero in the thermodynamic limit. This implies that, if one of the two random variables tends to a trivial one (i.e. delta-like distributed), then also the other does and, by consequence, the TNT picture should be dismissed. We identify the functional relation among the two variables using the method of the least squares which turns out to be a monotonically increasing function. Our results show that the two overlaps are completely equivalent in the description of the low temperature phase of the Edwards-Anderson model.

cond-mat.dis-nn↗

arXiv2005

Surface terms on the Nishimori line of the Gaussian Edwards-Anderson model

For the Edwards-Anderson model we find an integral representation for some surface terms on the Nishimori line. Among the results are expressions for the surface pressure for free and periodic boundary conditions and the adjacency pressure, i.e., the difference between the pressure of a box and the sum of the pressures of adjacent sub-boxes in which the box can been decomposed. We show that all those terms indeed behave proportionally to the surface size and prove the existence in the thermodynamic limit of the adjacency pressure.

math-ph↗

arXiv2005

The Ghirlanda-Guerra Identities

If the variance of a Gaussian spin-glass Hamiltonian grows like the volume the model fulfills the Ghirlanda-Guerra identities in terms of the normalized Hamiltonian covariance.

math-ph↗

arXiv2005

Factorization Properties in the 3D Edwards-Anderson Model

Starting from the study of a linear combination of multi-overlaps which can be rigorously shown to vanish for large systems we numerically analyze the factorization properties of the link-overlaps multi-distribution for the 3D Gaussian Edward-Anderson spin-glass model. We find evidence of a pure factorization law for the multi-correlation functions. For instance the quantity [ - ]/ tends to zero at increasing 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. The necessity of a better understanding of the mutual relation between the two overlaps is pointed out.

cond-mat.dis-nn↗

arXiv2004

Local Order at Arbitrary Distances in Finite-Dimensional Spin-Glass Models

For a finite dimensional spin-glass model we prove local order at low temperatures for both local observables and for products of observables at arbitrary mutual distance. When the Hamiltonian includes the Edwards-Anderson interaction we prove "bond" local order, when it includes the random-field interaction we prove "site" local order.

cond-mat.dis-nn↗