### Abstract

We consider two disordered lattice models on the square lattice: on the medial lattice the random field Ising model at T = 0 and on the direct lattice the random bond Potts model in the large-q limit at its transition point. The interface properties of the two models are known to be related by a mapping which is valid in the continuum approximation. Here we consider finite random samples with the same form of disorder for both models and calculate the respective equilibrium states exactly by using combinatorial optimization algorithms. We study the evolution of the interfaces with the strength of disorder and analyse and compare the interfaces of the two models in finite lattices.

Original language | English |
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Article number | P08027 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2010 |

Issue number | 8 |

DOIs | |

Publication status | Published - Jan 1 2010 |

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### Keywords

- Disordered systems (theory)
- Interfaces in random media (theory)
- Optimization over networks
- Self-affine roughness (theory)

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Journal of Statistical Mechanics: Theory and Experiment*,

*2010*(8), [P08027]. https://doi.org/10.1088/1742-5468/2010/08/P08027