Some aspects of infinite range models of spin glasses: theory and numerical simulations

These notes give an introduction to the physics of the infinite range version of the Edwards–Anderson model, the so-called Sherrington–Kirkpatrick model. In a first part, I motivate and introduce the Edwards–Anderson and Sherrington–Kirkpatrick models. In the second part, I explain the analytical solution of the Sherrington–Kirkpatrick model, following Giorgio Parisi. I next give the physical interpretation of this solution. This is a vast subject, and I concentrate on the major points and give references for more details. The third part presents the simulation approach and compare its results to theoretical expectations: thermodynamics, finite size scaling, determination of the critical temperature using “parameters” like the “Binder parameter”, and fluctuations. The last part gives a summary of our current understanding of finite size effects for the free energy and internal energy of the Sherrington–Kirkpatrick model