  We consider an Ising model with quenched surface disorder, the disorder
average of the free energy is the main object of interest. Explicit expressions
for the free energy distribution are difficult to obtain if the quenched
surface spins take values of $\pm 1$. Thus, we choose a different approach and
model the surface disorder by Gaussian random matrices. The distribution of the
free energy is calculated. We chose skew-circulant random matrices and
analytically compute the characteristic function of the free energy
distribution. From the characteristic function we numerically calculate the
distribution and show that it becomes log-normal for sufficiently large
dimensions of the disorder matrices, and in the limit of infinitely large
matrices tends to a Gaussian. Furthermore, we establish a connection to the
central limit theorem.
