A PCA approach to sourlas code analysis

The statistical mechanical approach is a powerful method for understanding large degrees of freedom problems, such as those related to the spin-glass model, but its application is usually limited to the class of mean-field models. We try a new general and computational approach - instead of an exact calculation of the Boltzmann distribution, we use an empirical spin state distribution obtained through simulation and extract potentially useful axes by principal component analysis (PCA). We adopted a three-body Sourlas code to evaluate this PCA approach compared with existing replica theory. The empirical spin distribution projected to these PCA axes showed distinctive patterns corresponding to the phase given by the replica method. Moreover, the first principal component roughly coincided with one of the order parameters (averaged spin) under a certain condition. These results suggest that this PCA approach could be effective even in more complicated systems that we cannot investigate analytically.