2010/05/31 by M. Karsai, M Karsai, J-Ch. Angles d'Auriac +3
Mathematics · Physics and Astronomy · #Ising model #Lattice (music) #Limit (mathematics) #Markov Chains and Monte Carlo Methods #Potts model #Random field #Square lattice #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamic limit #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2010/08/p08027
published in Journal of Statistical Mechanics Theory and Experiment 2010(08), P08027 (Institute of Physics) · 7 pages, 6 figures
arxiv created 2010/05/31 · openalex publication_date 2010/08/31 · arxiv updated 2015/05/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.