76301 - Statistical mechanics of Complex Systems

Learning outcomes

At the end of the course the student is familiar with the advanced notions on statistical mechanics topics and its socio-economic applications. He is able to investigate independently the novel topics of the discipline from research papers.

Course contents

-    Introductive lecture
-    Probability Spaces
-    Entropy
-    Simplexes and probability spaces.
-    Particle systems and Ising models.
-    Ising model in d=1 with free and periodic boundary conditions.
-    Dichotomic functions and their Fourier expansion. 
-    Simple notions for Ising models at d>1
-    The thermodynamic limit and correlation inequalities.
-    Mean field models. Curie-Weiss model.
-    Thermodynamic limit for mean field models.
-    The solution of the Curie Weiss model with boundary from above and below.
-    Large number theorem and central limit theorem for the magnetization. Free model and model with interaction.
-    Large deviation theory and solution of the Curie Weiss model.
-    Theoretical inverse problem: from thermodynamic quantities to parameters.
-    Phenomenological inverse problem: from real data to thermodynamic quantities.
-    Maximum likelihood method.

Readings/Bibliography

"Perspectives on Spin Glasses", Pierluigi Contucci e Cristian Giardina, Cambridge University Press

Teaching methods

Class lectures, examples, and exercises. Computer simulations illustrations. In case international students will be attending the course the lectures will be in english.

Assessment methods

The exam test is of oral type and possibly, if the student is interested, can take the form of a simple research seminar. The final grade will be computed as the average of two modules. The exam has the purpose to prove that the student has assimilated the fundamentals concepts and is able to develop rigorous proofs on the course content.

Teaching tools

Some lectures, especially those on the inverse problem, will be given by showing computer simulations  or data elaboration.

Links to further information

http://www.dm.unibo.it/~contucci/lectiones.html

Office hours

See the website of Pierluigi Contucci