Finite size corrections in the SK model
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
The finite size corrections to the SK model are important as they provide a clue as to what is the dimension below which the Parisi replica symmetry breaking picture of spin glasses no longer applies. We present arguments that the finite size correction to the free energy per spin scales like $1/N^4\mu$, the sample to sample fluctuation of the total free energy scales as $N^\mu$ and that the average number of peaks/features in the overlap function $P_J(q)$ also scales as $N^\mu$. Theoretical arguments and numerical evidence are given that the exponent $\mu$ is 1/6. With this value of $\mu$, six would appear to be the dimension below which the droplet/scaling picture is valid.