Monte Carlo Renormalization Group for Classical Lattice Models with Quenched Disorder

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• Real-space renormalization group (RNG) methods are crucial for studying critical phenomena.
• Applying RNG to disordered systems presents significant computational challenges.
• Existing methods struggle with long relaxation times in large disordered systems.

Purpose of the Study:

• To extend a variational RNG scheme to quenched-disordered systems.
• To enable computation of critical exponents in disordered models.
• To improve the efficiency of Monte Carlo simulations for these systems.

Main Methods:

• Developed a variational scheme for RNG calculations applicable to disordered systems.
• Introduced a bias potential, derived from minimizing a convex functional, to accelerate Monte Carlo relaxation.
• Analyzed the flow of the renormalized Hamiltonian distribution.

Main Results:

• The method provides access to the flow of the renormalized Hamiltonian distribution in quenched-disordered systems.
• Critical exponents can be computed if renormalized coupling correlations maintain finite range.
• Demonstrated significant reduction in Monte Carlo relaxation time for large disordered systems.

Conclusions:

• The extended variational RNG scheme is effective for analyzing quenched-disordered spin systems.
• The approach offers a computationally efficient way to study critical phenomena in complex magnetic models.
• Successful applications include the 2D dilute Ising model and random field Ising models in 2D and 3D.