Multicritical points for the spin glass models on hierarchical lattices

Details Multicritical points for the spin glass models on hierarchical lattices Multicritical points for the spin glass models on hierarchical lattices

2008-02-20

arxiv.org/abs/0802.2760v2

Phys. Rev. E 77, 061116 (2008)

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages, 9 figures, 7 tables This is the published version

Scientific paper

10.1103/PhysRevE.77.061116

The locations of multicritical points on many hierarchical lattices are numerically investigated by the renormalization group analysis. The results are compared with an analytical conjecture derived by using the duality, the gauge symmetry and the replica method. We find that the conjecture does not give the exact answer but leads to locations slightly away from the numerically reliable data. We propose an improved conjecture to give more precise predictions of the multicritical points than the conventional one. This improvement is inspired by a new point of view coming from renormalization group and succeeds in deriving very consistent answers with many numerical data.

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