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Critical interfaces in the random-bond Potts model.

Jesper L Jacobsen1, Pierre Le Doussal, Marco Picco

  • 1CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris, France.

Physical Review Letters
|March 5, 2009
PubMed
Summary
This summary is machine-generated.

We calculated the fractal dimension of interfaces in a disordered Potts model. Numerical and theoretical results for Fortuin-Kasteleyn (FK) domain walls and spin clusters are consistent with conformal field theory predictions.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Conformal field theory

Background:

  • The study of interfaces in disordered systems is crucial for understanding phase transitions.
  • Conformal field theory (CFT) provides a powerful framework for analyzing critical phenomena.
  • Quenched disorder introduces complexities not captured by standard CFT.

Purpose of the Study:

  • To investigate the geometrical properties of interfaces in the random-temperature q-states Potts model.
  • To compute the fractal dimension of Fortuin-Kasteleyn (FK) domain walls using conformal perturbation theory.
  • To compare theoretical predictions with numerical simulations for the fractal dimension of interfaces.

Main Methods:

  • Conformal perturbation theory applied to the q-states Potts model with q-2.
  • Numerical simulations using the Wolff cluster algorithm for q=3.
  • Transfer-matrix evaluations for calculating fractal dimensions.
  • Analysis of spin cluster interfaces for q=3.

Main Results:

  • The fractal dimension of FK domain walls was computed theoretically.
  • Numerical computations of the fractal dimension for FK domain walls and spin cluster interfaces were performed for q=3.
  • The numerical results for q=3 are consistent with the duality kappa_spin * kappa_FK = 16.
  • The findings support the application of CFT in disordered systems.

Conclusions:

  • The fractal dimension of interfaces in the disordered q-states Potts model can be accurately determined using both theoretical and numerical methods.
  • The results validate the use of conformal perturbation theory and highlight the importance of duality relations in understanding these systems.
  • The study contributes to the broader understanding of critical phenomena in the presence of quenched disorder.