Study of longitudinal fluctuations of the Sherrington-Kirkpatrick model

We study finite-size corrections to the free energy of the Sherrington-Kirkpatrick spin glass in the low-temperature phase where replica symmetry is broken. We investigate the role of longitudinal fluctuations in these corrections, neglecting the transverse contribution. In particular, we are interested in the value of exponent alpha that controls the finite volume corrections: alpha is defined by the relation f - f(infinity) similar to N-alpha, N being the total number of spins. We perform both an analytical and numerical estimate of the analytical result for alpha. From both the approaches, we get the result: alpha approximate to 0.8.