Study of longitudinal fluctuations of the Sherrington-Kirkpatrick spin glass

Spin glasses are disordered systems with a complex behavior, caused by the very high degeneracy of low energy states. They have a phase transition between a paramagnetic phase and a spin glass phase, in which the ergodicity is broken in a hierarchical organization of states. This implies many peculiar properties such as aging, remanence and memory effect. In our work, we study finite-size corrections to the mean field model, the Sherrington-Kirkpatrick spin glass, whose solution is well-known. The behavior of these corrections in the low temperature phase has been debated for several years. Because of the complicated form of the theory around the mean field solution and of the difficulty to perform a numerical estimate, no final value has been found so far. We investigate the role of longitudinal fluctuations, neglecting the transverse contribution. Since they can be calculated directly into the full-replica symmetry breaking ansatz, it is easier to obtain a prediction for their behavior.