### 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 - 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

- Statistics and Probability
- Statistical and Nonlinear Physics
- 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

**Interface mapping in two-dimensional random lattice models.** / Karsai, M.; D'Auriac, J. Ch Anglès; Iglói, F.

Research output: Contribution to journal › Article

*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2010, no. 8, P08027. https://doi.org/10.1088/1742-5468/2010/08/P08027

}

TY - JOUR

T1 - Interface mapping in two-dimensional random lattice models

AU - Karsai, M.

AU - D'Auriac, J. Ch Anglès

AU - Iglói, F.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Disordered systems (theory)

KW - Interfaces in random media (theory)

KW - Optimization over networks

KW - Self-affine roughness (theory)

UR - http://www.scopus.com/inward/record.url?scp=77957574877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957574877&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2010/08/P08027

DO - 10.1088/1742-5468/2010/08/P08027

M3 - Article

AN - SCOPUS:77957574877

VL - 2010

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 8

M1 - P08027

ER -