Calendário de Eventos

Colóquio da Pós-Graduação - Prof. Sérgio Magalhães (UFRGS)
Quinta-feira, Dezembro 02, 2021, 16:00
por Mariana de Carvalho Ilheo
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Título: "Giorgio Parisi: Spin glasses, complexity and all that"

Palestrante: Prof. Sérgio Magalhães (Universidade Federal do Rio Grande do Sul) 


In this seminar, I present the contributions made by Giorgio Parisi in disordered complex systems which granted to him the Nobel prize 2021. Indeed, the theory created by Parisi to deal with disordered complex systems has generated such an overpowering conceptual framework that it spilled over into other areas of knowledge as distinct as mathematics, biology, neuroscience, and computation. The starting point, according to Parisi himself [1], is that disorder generates complexity. In that sense, the spin-glass systems discovered in the mid of 70's last century served as the suitable platform to unveil this relationship between disorder and complexity. Therefore, I explain some experimental aspects of the spin-glass problem in order to situate the problem and the level of difficulty for its description. Next, I discuss theoretical attempts which, although failed to provide a satisfactory description of the original problem, introduced some fundamental technical aspects such as the replica method. In particular, it is reviewed the mean-field Sherrington-Kirkpatrick theory and replica symmetry solution. Then, I move to the famous Parisi solution for breaking the replica symmetry. Firstly showing the one-step replica symmetry breaking (RSB) and the final formulation, the so-called full step RSB. Next, it is examined the nature of the spin-glass phase that emerges from the Parisi solution and the concept of ultrametricity. With that, I give a brief summary of the use of Parisi's theory beyond physics. Finally, the actuality of the Parisi solution is debated in view of the discovery of the presence of spin glass-like phases in several condensed matter systems that are currently being studied.

[1] G. Parisi, Physica A, 194 28-40 (1993).


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