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We present an analysis leading to precise locations of the multicriticalpoints for spin glasses on regular lattices. The conventional technique fordetermination of the location of the multicritical point was previously derivedusing a hypothesis emerging from duality and the replica method. In the presentstudy, we propose a systematic technique, by an improved technique, giving moreprecise locations of the multicritical points on the square, triangular, andhexagonal lattices by carefully examining relationship between two partitionfunctions related with each other by the duality. We can find that themulticritical points of the $\pm J$ Ising model are located at $p_c = 0.890813$on the square lattice, where $p_c$ means the probability of $J_{ij} = J(>0)$,at $p_c = 0.835985$ on the triangular lattice, and at $p_c = 0.932593$ on thehexagonal lattice. These results are in excellent agreement with recentnumerical estimations.

Locations of multicritical points for spin glasses on regular lattices