Programma dettagliato e risultati di apprendimento attesi
Complex systems are encountered in a variety of situations and one of the accepted fingerprint of complexity is the presence of power laws in the probability distributions of the relevant quantities, whose bursty dynamics generates a linear trend in a bilogaritmic plot. This is in contrast with the usual relaxation behavior of classical systems, where the fluctuations are described in terms of the Gaussian distribution. A unified theory of systems showing power law behavior is still lacking. For this reason many theoretical attempts are presently under development and this field of research literally exploded over the last decades.
The programme of the course will start with a series of lectures given by Prof. Ezio Puppin on the basic concepts of equilibrium statistical physics of non interacting particles in the Gibbs formulation. After that the effects of a weak interaction between particles will be discussed both for classical systems (van der Waals equation, cluster expansion) and quantum systems (quasiparticles and second quantization).
The secon part, given by Prof. Paolo Biscari, will consist in increasing the strength of the interaction by allowing the occurrence of phase transitions. The discussion will be mostly based on the Ising model that will be tackled both in terms of simulations and from the mean field theory point of view, with a special emphasis on the fluctuations at the critical point. The role of quenched disorder will be discussed in connection with the physics of spin glasses and in terms of the random field Ising model.
In the numerical lab, under the supervision of Prof. Stefano Turzi, after a brief introduction of their mathematical foundations, the candidates will have the opportunity of getting acquainted with Monte-Carlo methods, specifically, Markov Chain Monte Carlo and Metropolis algorithm. This method will be applied to the study of phase transitions for the Ising model, in 1D and 2D, where critical slowing-down and finite-scale effects will be discussed. Finally, we will consider a cluster algorithm (Wolff) as a method to improve convergence close to the phase transition.
Note Sulla Modalità di valutazione
The exam will consist of two parts:
- The first part will be the developments of a code, using Mathematica, for performing Monte Carlo calculations of a system of interacting particle.
- The second part will be in written form and will consist of an in-depth study of a topic related to those of the course.
Intervallo di svolgimento dell'attività didattica
Calendario testuale dell'attività didattica
Lectures given by Prof. Ezio Puppin
09 march 2021 (14:30 - 17:30)
16 march 2021 (14:30 - 17:30)
19 march 2021 (14:30 - 17:30)
Lectures given by Prof. Paolo Biscari
23 march 2021 (09:00 - 12:00)
25 march 2021 (09:00 - 12:00)
26 march 2021 (09:00 - 12:00)
Numerical lab with Prof. Stefano Turzi
26 march 2021 (14:30 - 16:30)
29 march 2021 (14:30 - 16:30)
30 march 2021 (14:30 - 16:30)
01 april 2021 (14:30 - 16:30)
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