• Corpus ID: 119320407

On the Absence of Replica Symmetry Breaking and Decay of Correlations in the Random Field Ising Model

@article{Roldan2018OnTA,
  title={On the Absence of Replica Symmetry Breaking and Decay of Correlations in the Random Field Ising Model},
  author={Jamer Roldan and Roberto Vila},
  journal={arXiv: Mathematical Physics},
  year={2018}
}
This work is concerned with the theory of the Random Field Ising Model with presence of special non-Gaussian random fields on the hypercubic and hexagonal lattices. On the hypercubic lattice, we shown the absence of replica symmetry in any dimensions, at any temperature and field strength, almost surely. On the hexagonal lattice we obtained the decay ratio of the correlations. 
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References

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Replica Symmetry Breaking in the Random Field Ising Model

We discuss the critical behavior of the random field Ising model, using techniques of replica symmetry breaking familiar from the theory of spin glasses and random manifolds. Using an approximation…

Absence of Replica Symmetry Breaking in the Random Field Ising Model

It is shown that replica symmetry is not broken in the random field Ising model in any dimension, at any temperature and field strength, except possibly at a measure-zero set of exceptional…

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TLDR
For random-field models, this work rigorously proves uniqueness of the Gibbs state 2D Ising systems, and absence of continuous symmetry breaking in the Heisenberg model in d\ensuremath{\le}4, as predicted by Imry and Ma.