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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Renormalization group (RG) methods are crucial for understanding phase transitions.
  • Their application to quenched disordered systems remains challenging.
  • Investigating simplified models offers insights into complex phenomena.

Purpose of the Study:

  • To explore the phase transition in quenched disordered systems.
  • To apply real-space RG methods to a specific model.
  • To accurately determine critical exponents at zero temperature.

Main Methods:

  • Real-space renormalization group (RG) transformation.
  • Dyson hierarchical lattice model with a random field.
  • Evaluation of critical exponents at T=0.
  • Comparison with an independent method for validation.

Main Results:

  • Reconstruction of the RG flow in the studied model.
  • Accurate estimation of critical exponents at T=0.
  • Validation of the RG method's efficacy through comparison.

Conclusions:

  • The real-space RG method provides accurate critical exponent estimations for quenched disordered systems.
  • This approach offers a viable way to understand complex phase transitions.
  • The findings contribute to the theoretical understanding of disordered systems.