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arXiv:2305.10670

Nonsingular increase in magnetic susceptibility and transition in universality in site-diluted Ising model in two dimensions

Eduardo C. Cuansing

Published May 18, 2023• 0 citations
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Abstract

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 $M$ per spin, energy $E$ per spin, magnetic susceptibility $χ$ per spin, and specific heat $C$ per spin are then calculated after the system has equilibrated. At small dilution concentrations $d<0.1$, we find that the value of the critical exponent $β$ does not deviate from its pure Ising value. At higher dilution concentrations $d>0.1$, however, we find $β$ to strongly depend on the value of $d$. We are able to locate a critical temperature $T_c$ and a critical dilution concentration $d_c$ where the phase transition occurs. We find $T_c$ to depend linearly on $d$. In the phase diagrams of $M$, $E$, $χ$, and $C$, 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 $χ$ at the low temperature and high dilution region.

DOI
10.48550/arxiv.2305.10670

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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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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.
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