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arXiv:2609.36886

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

Alexandros Vasilopoulos, Zeynep Demir Vatansever, Erol Vatansever, G. T. Barkema, Nikolaos G. Fytas

Published Sep 29, 2026• 0 citations
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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.

DOI
10.48550/arxiv.2609.36886

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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=1ν= 1ν=1 and γ/ν=7/4γ/ν= 7/4γ/ν=7/4 retain their exact pure Ising values for all spin concentrations ppp considered, consistent with the marginal irrelevance of disorder at α=0α= 0α=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, zzz decreases upon dilution on both lattice, opposite to what is observed under local dynamics, with evidence of saturation to a ppp-independent value at strong dilution, suggesting a diluted dynamic fixed point. While zzz 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.
We study the effects of dilution to the critical properties of site-diluted Ising model in two dimensions using Monte Carlo simulations. Quenched disorder from the dilution is incorporated into the Ising model via random empty sites on the square lattice of Ising spins. Thermodynamic quantities such as the magnetization MMM per spin, energy EEE per spin, magnetic susceptibility χχχ per spin, and specific heat CCC per spin are then calculated after the system has equilibrated. At small dilution concentrations d<0.1d<0.1d<0.1, we find that the value of the critical exponent βββ does not deviate from its pure Ising value. At higher dilution concentrations d>0.1d>0.1d>0.1, however, we find βββ to strongly depend on the value of ddd. We are able to locate a critical temperature TcT_cTc​ and a critical dilution concentration dcd_cdc​ where the phase transition occurs. We find TcT_cTc​ to depend linearly on ddd. In the phase diagrams of MMM, EEE, χχχ, and CCC, we find that the phase transition line eventually disappears at high dilutions. Our results suggest that there is a transition from Strong Universality at low dilution to Weak Universality at high dilution. Lastly, we find a wide and nonsingular increase in the magnetic susceptibility χχχ at the low temperature and high dilution region.
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Abstract We have studied the critical properties of the contact process on a square lattice with quenched site dilution by Monte Carlo simulations. This was achieved by generating in advance the percolating cluster, through the use of an appropriate epidemic model, and then by the simulation of the contact process on the top of the percolating cluster. The dynamic critical exponents were calculated by assuming an activated scaling relation and the static exponents by the usual power law behavior. Our results are in agreement with the prediction that the quenched diluted contact process belongs to the universality class of the random transverse-field Ising model. We have also analyzed the model and determined the phase diagram by the use of a mean-field theory that takes into account the correlation between neighboring sites.
We perform extensive Monte Carlo simulations to investigate the dynamic phase transition properties of the two-dimensional kinetic Ising model on the kagome lattice in the presence of square-wave oscillating magnetic field. Through detailed finite-size scaling analysis, we study universality aspects of the nonequilibrium phase transition. Obtained critical exponents indicate that the two-dimensional kagome-lattice kinetic Ising model belongs to the same universality class with the corresponding Ising model in equilibrium. Moreover, dynamic critical exponent of the local moves used in simulations is determined with high precision. Our numerical results are compatible with the previous ones on kinetic Ising models.
Monte Carlo cluster algorithms are popular for their efficiency in studying the Ising model near its critical temperature. We might expect that this efficiency extends to the bond-diluted Ising model. We show, however, that this is not always the case by comparing how the correlation times τ_{w} and τ_{sw} of the Wolff and Swendsen-Wang cluster algorithms scale as a function of the system size L when applied to the two-dimensional bond-diluted Ising model. We demonstrate that the Wolff algorithm suffers from a much longer correlation time than in the pure Ising model, caused by isolated (groups of) spins which are infrequently visited by the algorithm. With a simple argument we prove that these cause the correlation time τ_{w} to be bounded from below by L^{z_{w}} with a dynamical exponent z_{w}=γ/ν≈1.75 for a bond concentration p<1. Furthermore, we numerically show that this lower bound is actually taken for several values of p in the range 0.5<p<1. Moreover, we show that the Swendsen-Wang algorithm does not suffer from the same problem. Consequently, it has a much shorter correlation time, shorter than in the pure Ising model even. Numerically at p=0.6, we find that its dynamical exponent is z_{sw}=0.09(4).