Infinitely Robust Order and Local Order-Parameter Tulips in Apollonian Networks with Quenched Disorder

TL;DR

This paper demonstrates that various quenched random spin systems on Apollonian networks maintain ordered phases at infinite temperature, revealing complex tulip patterns in local order parameters through a detailed renormalization-group analysis.

Contribution

It introduces a renormalization-group method that provides exact distributions of local magnetizations and spin-glass order parameters in disordered Apollonian networks.

Findings

Ordered phases persist at infinite temperature across disorder types

Local order parameters exhibit complex tulip patterns

Exact distributions of local magnetizations and spin-glass parameters are obtained

Abstract

For a variety of quenched random spin systems on an Apollonian network, including ferromagnetic and antiferromagnetic bond percolation and the Ising spin glass, we find the persistence of ordered phases up to infinite temperature over the entire range of disorder. We develop a renormalization-group technique that yields highly detailed information, including the exact distributions of local magnetizations and local spin-glass order parameters, which turn out to exhibit, as function of temperature, complex and distinctive tulip patterns.