The Random-bond Potts model in the large-q limit

Abstract

We study the critical behavior of the q-state Potts model with random ferromagnetic couplings. Working with the cluster representation the partition sum of the model in the large-q limit is dominated by a single graph, the fractal properties of which are related to the critical singularities of the random Potts model. The optimization problem of finding the dominant graph, is studied on the square lattice by simulated annealing and by a combinatorial algorithm. Critical exponents of the magnetization and the correlation length are estimated and conformal predictions are compared with numerical results.

7 pages, 6 figures

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Cited by in corpus (12)

• Strong disorder RG approach of random systems
• Disorder induced rounding of the phase transition in the large q-state Potts model
• Critical and tricritical singularities of the three-dimensional random-bond Potts model for large $q$
• High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials
• Global disorder transition in the community structure of large-q Potts systems
• The stability to instability transition in the structure of large scale networks
• Phase-transitions of the random bond Potts chain with long-range interactions
• Rounding of first-order phase transitions and optimal cooperation in scale-free networks
• Optimal Cooperation and Submodularity for Computing Potts' Partition Functions with a Large Number of State
• Density of critical clusters in strips of strongly disordered systems
• Excess entropy and central charge of the two-dimensional random-bond Potts model in the large-Q limit
• Interface mapping in two-dimensional random lattice models