An analytical application of Niedermayer's algorithm to the Edwards-Anderson model: analytical results for the multicritical point on the Nishimori line

We apply analytically Niedermayer's algorithm to the Edwards-Anderson model on random graphs with arbitary degree distributions. The results for the multicritical point on the Nishimori line are shown. The results are shown by applying a criterion for spin models on the random graphs with arbitary degree distributions. The application of Niedermayer's algorithm makes the size of the Fortuin-Kasteleyn cluster small and shifts the percolation threshold. The results for the $\pm J$ model and the Gaussian model are respectively shown. In the present article, it is respectively shown for the $\pm J$ model and the Gaussian model that, by adjusting an introduced parameter for Niedermayer's algorithm, the percolation threshold obtained in the present article agrees with the location of the multicritical point. We naively estimate the locations of the multicritical points for the $\pm J$ model and the Gaussian model on the randam graphs with arbitary degree distributions.