Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices

Details Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices Location of the Multicritical Point for the Ising Spin Glass on the Triangular and Hexagonal Lattices

2006-01-17

arxiv.org/abs/cond-mat/0601356v2

J. Phys. Soc. Jpn. 75 (2006) 034004

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, 1 figure; Minor corrections in notation

Scientific paper

10.1143/JPSJ.75.034004

A conjecture is given for the exact location of the multicritical point in the phase diagram of the +/- J Ising model on the triangular lattice. The result p_c=0.8358058 agrees well with a recent numerical estimate. From this value, it is possible to derive a comparable conjecture for the exact location of the multicritical point for the hexagonal lattice, p_c=0.9327041, again in excellent agreement with a numerical study. The method is a variant of duality transformation to relate the triangular lattice directly with its dual triangular lattice without recourse to the hexagonal lattice, in conjunction with the replica method.

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