Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2008-11-04
Phys. Rev. E 79, (2009) 021129
Physics
Condensed Matter
Disordered Systems and Neural Networks
17pages, this is the published version with some minnor corrections. Previous title was "Precise locations of multicritical po
Scientific paper
10.1103/PhysRevE.79.021129
We present an analysis leading to precise locations of the multicritical points for spin glasses on regular lattices. The conventional technique for determination of the location of the multicritical point was previously derived using a hypothesis emerging from duality and the replica method. In the present study, we propose a systematic technique, by an improved technique, giving more precise locations of the multicritical points on the square, triangular, and hexagonal lattices by carefully examining relationship between two partition functions related with each other by the duality. We can find that the multicritical 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 the hexagonal lattice. These results are in excellent agreement with recent numerical estimations.
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