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This study investigates critical behavior in two-dimensional Potts models with power-law decaying bond disorder. Researchers found evidence of a crossover between universality classes, impacting understanding of magnetic systems.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Quantum Field Theory

Background:

  • Two-dimensional Potts models are crucial for understanding phase transitions.
  • Previous work explored the thermal sector using renormalization group methods.
  • Disorder effects, particularly power-law decaying correlations, present unique challenges.

Purpose of the Study:

  • To investigate the magnetic sector of two-dimensional Potts models with power-law bond disorder.
  • To compute leading corrections to the Potts spin scaling dimension.
  • To provide numerical evidence for a crossover between universality classes.

Main Methods:

  • Renormalization group computation based on perturbed conformal field theory.
  • Analysis of the magnetic sector, extending previous thermal sector investigations.
  • Comparison of theoretical predictions with Monte Carlo simulations.

Main Results:

  • Calculation of leading corrections to the Potts spin scaling dimension.
  • Inclusion of the long-range disorder Ising model as a special case.
  • Observation of a crossover in the magnetization scaling function between long-range and short-range universality classes.

Conclusions:

  • The renormalization group approach effectively probes the magnetic sector of disordered Potts models.
  • Theoretical predictions align with Monte Carlo simulation results.
  • Clear numerical evidence supports a crossover phenomenon in universality classes due to disorder correlation length.