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We developed a new replica method to study critical systems with quenched bond randomness. This method reveals a line of renormalization group fixed points, solving long-standing puzzles in random fixed point theories.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Quantum field theory

Background:

  • Critical systems with quenched disorder present significant theoretical challenges.
  • Understanding the behavior of the q-state Potts model with random bonds is crucial.

Purpose of the Study:

  • To introduce an exact replica method for studying critical systems with quenched bond randomness in 2D.
  • To analyze the renormalization group fixed points of the q-state Potts model with quenched disorder.

Main Methods:

  • Exact replica method
  • Renormalization group analysis
  • Study of the q-state Potts model

Main Results:

  • A line of renormalization group fixed points interpolating between weak and strong randomness was identified.
  • A q-independent sector was found within the theory.
  • The correlation length exponent retains the Ising value, while the magnetization exponent and effective central charge vary continuously.

Conclusions:

  • The findings resolve long-standing numerical and theoretical puzzles in the field.
  • The study illustrates unique characteristics of conformal field theories for random fixed points.
  • The developed replica method provides a powerful tool for future research in disordered systems.