Analysis method combining Monte Carlo simulation and principal component analysis - Application to Sourlas code

The replica method (RM) provides an accurate evaluation of a class of mean-field (MF) models in the thermodynamic limit. It is, however, not straightforward to extend its application to a class of non-MF models and finite-size models with sufficient accuracy. We previously proposed a numerical approach as an alternative, in which principal component analysis (PCA) is employed to analyze configurations sampled through Monte Carlo simulations. Using this method, we examine both two- and three-body mean-field Sourlas codes as a test board and compare our results with those of the RM. We confirm that the spin distribution map constructed using PCA axes has specific characteristics approximately corresponding to the phases given by RM. This result suggests that the PCA approach will be effective even with general non-MF finite-size models.