Multicritical points for the spin glass models on hierarchical lattices

Abstract

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.

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

References in corpus (1)

• Multicritical Point Relations in Three Dual Pairs of Hierarchical-Lattice Ising Spin-Glasses

Cited by in corpus (5)

• Locations of multicritical points for spin glasses on regular lattices
• On locations and properties of the multicritical point of Gaussian and +/-J Ising spin glasses
• Infinitely Robust Order and Local Order-Parameter Tulips in Apollonian Networks with Quenched Disorder
• Disordered Potts model on the diamond hierarchical lattice: Numerically exact treatment in the large-q limit
• Critical and multicritical behavior of the +- J Ising model in two and three dimensions