Dynamical real-space renormalization group calculations with a highly connected clustering scheme on disordered...

Area of Science:

• Statistical physics
• Network science
• Computational physics

Background:

• Conventional clustering methods like the Migdal-Kadanoff bond moving process often overlook network connectivity.
• Understanding critical phenomena in complex networks requires accurate calculation of exponents.

Purpose of the Study:

• Introduce a novel clustering scheme that preserves network connectivity.
• Evaluate the performance of this new scheme against conventional methods for critical phenomena analysis.
• Investigate the phase diagram and critical behavior of diluted lattices and hierarchical networks.

Main Methods:

• Development of a connectivity-preserving clustering scheme.
• Application of the scheme to the kinetic Ising model in various dimensions (d=2, 3, and high dimensions).
• Analysis of randomly bond diluted lattices and hierarchical lattices with different degree distributions.

Main Results:

• The new clustering scheme demonstrates superior performance in calculating correlation length and dynamical critical exponents in high dimensions compared to the Migdal-Kadanoff method.
• Dynamical critical exponents for the kinetic Ising model were found to be z=2.13 in 2D and z=2.09 in 3D, aligning well with Monte Carlo simulation results.
• Exact values for correlation and dynamical critical exponents were determined for hierarchical lattices.

Conclusions:

• The proposed connectivity-preserving clustering scheme offers a more accurate approach for studying critical phenomena in networks.
• The findings provide valuable insights into the behavior of diluted and hierarchical networks.
• This method enhances the analysis of critical exponents in statistical physics models.