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

TL;DR

This study uses exact renormalization-group methods to analyze three dual pairs of hierarchical-lattice Ising spin-glasses, confirming a conjecture relating multicritical points across dual lattices with high accuracy despite topological differences.

Contribution

It provides the first precise verification of a conjecture linking multicritical points in dual hierarchical-lattice spin-glasses using extensive numerical analysis.

Findings

The conjecture is realized with high accuracy across all dual pairs.

Reentrant behavior observed near multicritical points in all phase diagrams.

In lower-dimensional models, the spin-glass phase is absent and phase boundaries show non-universal critical behavior.

Abstract

The Ising spin-glasses are investigated on three dual pairs of hierarchical lattices, using exact renormalization-group transformation of the quenched bond probability distribution. The goal is to investigate a recent conjecture which relates, on such pairs of dual lattices, the locations of the multicritical points, which occur on the Nishimori symmetry line. Towards this end we precisely determine the global phase diagrams for these six hierarchical spin-glasses, using up to 2.5 x 10^9 probability bins to represent the quenched distribution subjected to an exact renormalization-group transformation. We find in all three cases that the conjecture is realized to a very good approximation, even when the mutually dual models belong to different spatial dimensionalities d and have different phase diagram topologies at the multicritical points of the conjecture and even though the contributions to the conjecture from each lattice of the dual pair are strongly asymmetric. In all six phase diagrams, we find reentrance near the multicritical point. In the models with d=2 or 1.5, the spin-glass phase does not occur and the phase boundary between the ferromagnetic and paramagnetic phases is second order with a strong violation of universality. PACS numbers: 75.10.Nr, 64.60.Kw, 05.45.Df, 05.10.Cc