Disorder averaging and finite-size scaling

Area of Science:

• Statistical Physics
• Condensed Matter Physics
• Computational Physics

Background:

• Disordered systems present challenges for traditional renormalization group (RG) methods.
• Existing RG approaches often renormalize averaged free energy, obscuring system-specific critical behavior.

Purpose of the Study:

• To propose a novel RG framework that accounts for disorder by analyzing individual random samples.
• To investigate the impact of this new approach on finite-size scaling in disordered systems.

Main Methods:

• Developed a new renormalization group (RG) picture considering individual random sample trajectories.
• Applied the new RG approach to study the finite-size scaling of the 2D random-bond Ising model.
• Compared results with traditional RG methods based on averaged free energy.

Main Results:

• Demonstrated that averaging over randomness should occur after determining the critical point for each realization.
• Identified sample-to-sample fluctuations in critical temperature as the cause of previously observed finite-size corrections.
• Showed that scaling predictions are accurately fulfilled only by the new averaging method.

Conclusions:

• The proposed RG approach provides a more accurate description of critical phenomena in disordered systems.
• This method correctly accounts for sample-to-sample fluctuations, leading to improved finite-size scaling predictions.
• The findings necessitate a re-evaluation of established RG techniques for disordered materials.