Spontaneous Magnetization in the Disorder dominated Phase of the Twodimensional Random Bond Ising Model

TL;DR

This paper extends the 2D random bond Ising model to include additional degrees of freedom, revealing a new phase with spontaneous magnetization characterized by an exponential decay of correlations.

Contribution

It introduces a full lattice theory with four real fermions, uncovering a novel phase between ferromagnetic and paramagnetic states not captured by previous renormalization-group approaches.

Findings

Discovery of a new phase with spontaneous magnetization

Correlation length inversely proportional to the square of the order parameter

Extension of the self-consistent approach to full lattice theory

Abstract

The selfconsistent approach to the 2D Ising Model with quenched random bonds is extended to the full lattice theory of four real fermions. The additional degrees of freedom, neglected in the renormalization-group theory, lead to a new phase between the ferromagnetic and the paramagnetic phase. The disorder averaged spin-spin correlation function decays exponentially with distance. The corresponding correlation length is $1/\eta^2$, where $\eta$ denotes the order parameter of the new phase introduced by Ziegler.