Asymptotic dynamic universality of diluted kagome and square lattices

Confirm whether the lattice-dependent dynamic critical exponents observed for the site-diluted Ising model under Wolff single-cluster dynamics are only finite-size crossover effects by simulating substantially larger systems or systematically studying the dynamic exponent z as the site concentration approaches the percolation threshold from above on both the kagome and square lattices.

Background

The paper finds that the dynamic critical exponent z is consistent between the kagome and square lattices in the pure Ising case but differs between them after site dilution. The authors interpret this difference as a finite-size crossover caused by the distinct percolation thresholds of the two lattices, rather than as evidence of genuinely different asymptotic dynamic universality classes.

The proposed renormalization-group picture connects the pure Ising fixed point to the percolation fixed point. Under this interpretation, the true asymptotic dynamic exponent should ultimately coincide on both lattices, but the available simulations cannot establish this conclusively. Resolving the issue requires substantially larger system sizes or a systematic investigation as the occupation probability approaches the respective percolation threshold from above.