Static versus dynamic universality in the site-diluted kagome Ising model

Abstract

We study the site-diluted Ising model on the kagome lattice using the Wolff single-cluster algorithm, focusing on both equilibrium and dynamic critical properties. The equilibrium critical exponents $ν= 1$ and $γ/ν= 7/4$ retain their exact pure Ising values for all spin concentrations $p$ considered, consistent with the marginal irrelevance of disorder at $α= 0$, with the specific heat crossing over from logarithmic to double-logarithmic growth upon dilution. These static results are shared between the kagome and square lattices. On the dynamic side, $z$ decreases upon dilution on both lattice, opposite to what is observed under local dynamics, with evidence of saturation to a $p$-independent value at strong dilution, suggesting a diluted dynamic fixed point. While $z$ is consistent between the two lattices in the pure case, it differs in the diluted regime, an effect we attribute to the two lattices sitting at different positions along the renormalization-group flow between the Ising and percolation fixed points, rather than to a true asymptotic breakdown of dynamic universality.