# Quenched bond dilution in two-dimensional Potts models

@article{Chatelain2001QuenchedBD, title={Quenched bond dilution in two-dimensional Potts models}, author={Christophe Chatelain and Bertrand Berche and Lev N. Shchur Henri Poincar'e University and Nancy and Institut fur Theoretische Physik and Universitat Leipzig and Landau Institute and Chernogolovka}, journal={Journal of Physics A}, year={2001}, volume={34}, pages={9593-9614} }

We report a numerical study of the bond-diluted two-dimensional Potts model using transfer-matrix calculations. For different numbers of states per spin, we show that the critical exponents at the random fixed point are the same as in self-dual random-bond cases. In addition, we determine the multifractal spectrum associated with the scaling dimensions of the moments of the spin-spin correlation function in the cylinder geometry. We show that the behaviour is fully compatible with the one…

## 11 Citations

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## References

SHOWING 1-10 OF 53 REFERENCES

Short-Time Dynamics of Random-Bond Potts Ferromagnet with Continuous Self-Dual Quenched Disorders*

- Physics
- 2002

We present our Monte Carlo results of the random-bond Potts ferromagnet with the Olson–Young self-dual distribution of quenched disorders in two dimensions. By exploring the short-time scaling…

Magnetic critical behavior of two-dimensional random-bond Potts ferromagnets in confined geometries.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1999

A numerical study of two-dimensional random-bond Potts ferromagnets, and the critical behavior is investigated through conformal invariance techniques that were recently shown to be valid, even in the randomness-induced second-order phase transition regime Q>4.

Universality and multifractal behaviour of spin–spin correlation functions in disordered Potts models

- Physics
- 1999

CRITICAL BEHAVIOR OF RANDOM-BOND POTTS MODELS

- Physics
- 1997

The effect of quenched impurities on systems which undergo first-order phase transitions is studied within the framework of the q-state Potts model. For large q a mapping to the random field Ising…

Finite-size scaling study of two-dimensional dilute Potts models

- Physics
- 1987

The author uses transfer matrices to calculate the free energy and various thermodynamic quantities of the two- and three-state Potts models with random bond interactions at the critical temperature.…

Renormalisation-group calculation of correlation functions for the 2D random bond Ising and Potts models

- Physics
- 1995

Finite-Size Scaling Study of the Surface and Bulk Critical Behavior in the Random-Bond Eight-State Potts Model

- Physics
- 1998

The self-dual random-bond eight-state Potts model is studied numerically through large-scale Monte Carlo simulations using the Swendsen-Wang cluster flipping algorithm. We compute bulk and surface…

Large-q asymptotics of the random-bond potts model

- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

Numerically examine the large-q asymptotics of the q-state random bond Potts model and finds that the central charge seems to behave like c(q)=1 / 2 log(2)(q)+O(1).