Frustrating and Diluting Dynamical Lattice Ising Spins

TL;DR

This paper studies how introducing annealed bond disorder affects the third order ferromagnetic phase transition in the Ising model on dynamical planar lattices and Feynman diagrams, revealing complex disorder effects.

Contribution

It explores the impact of annealed bond disorder on phase transitions in the Ising model on dynamical lattices and Feynman diagrams, a novel investigation in this context.

Findings

Disorder modifies the nature of phase transitions.

Antiferromagnetic and null couplings influence critical behavior.

Results suggest complex interplay between disorder and lattice dynamics.

Abstract

We investigate what happens to the third order ferromagnetic phase transition displayed by the Ising model on various dynamical planar lattices (ie coupled to 2D quantum gravity) when we introduce annealed bond disorder in the form of either antiferromagnetic couplings or null couplings. We also look at the effect of such disordering for the Ising model on general $\phi^3$ and $\phi^4$ Feynman diagrams.