Multicritical points for the spin glass models on hierarchical lattices

TL;DR

This paper investigates the precise locations of multicritical points in spin glass models on hierarchical lattices using renormalization group analysis, compares results with existing conjectures, and proposes an improved predictive conjecture.

Contribution

The paper introduces an improved conjecture for predicting multicritical points that aligns more closely with numerical data, surpassing traditional methods.

Findings

Existing conjecture slightly inaccurate compared to numerical data.

Proposed improved conjecture yields more precise predictions.

Results are consistent with numerous numerical simulations.

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.