Ising Spin Glasses on Wheatstone-Bridge Hierarchical Lattices

TL;DR

This paper investigates Ising spin glasses on Wheatstone-Bridge hierarchical lattices, revealing the lower critical dimension exceeds 2.32 and identifying finite-temperature spin-glass phases in lattices with fractal dimensions around 3.58 and near five.

Contribution

It demonstrates the existence of finite-temperature spin-glass phases on specific hierarchical lattices and estimates their critical dimensions, advancing understanding of spin-glass behavior in complex structures.

Findings

Lower critical dimension > 2.32

Finite-temperature spin-glass phases found at D ≈ 3.58 and near 5

Hierarchical lattices exhibit distinct spin-glass properties

Abstract

Nearest-neighbor-interaction Ising spin glasses are studied on three different hierarchical lattices, all of them belonging to the Wheatstone-Bridge family. It is shown that the spin-glass lower critical dimension in these lattices should be greater than 2.32. Finite-temperature spin-glass phases are found for a lattice of fractal dimension $D \approx 3.58$ (whose unit cell is obtained from a simple construction of a part of the cubic lattice), as well as for a lattice of fractal dimension close to five.