Two-dimensional random-bond Ising model, free fermions, and the network model

@article{Merz2002TwodimensionalRI,
  title={Two-dimensional random-bond Ising model, free fermions, and the network model},
  author={Florian Merz and J. T. Chalker},
  journal={Physical Review B},
  year={2002},
  volume={65},
  pages={054425}
}
We develop a recently proposed mapping of the two-dimensional Ising model with random exchange (RBIM) via the transfer matrix, to a network model for a disordered system of noninteracting fermions. The RBIM transforms in this way to a localization problem belonging to one of a set of nonstandard symmetry classes, known as class D; the transition between paramagnet and ferromagnet is equivalent to a delocalization transition between an insulator and a quantum Hall conductor. We establish the… 
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TLDR
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