Equilibriumlike invaded cluster algorithm: Critical exponents and dynamical properties

We present a detailed study of the equilibriumlike invaded cluster algorithm, recently proposed as an extension of the invaded cluster algorithm, designed to drive the system to criticality while still preserving the equilibrium ensemble. We perform extensive simulations on two special cases of the Potts model and examine the precision of critical exponents by including the leading corrections. We show that both thermal and magnetic critical exponents can be obtained with high accuracy compared to the best available results. The choice of the auxiliary parameters of the algorithm is discussed in context of dynamical properties. We also discuss the relation to the Li-Sokal bound for the dynamical exponent $z$.

Figure 1

(Color online) Overlap fits of energy distributions $w\left(e\right)$ for $q=3$ Potts in 2D rescaled with the exact exponent $X=0.8$. In the inset are shown ln-ln plots of $L^d\text{var}\left(e\right)$ vs $L$. The statistic is ${10}^6$ MCS for both EIC and IC cases, and the parameters of the EIC algorithm were chosen to be $N_a=100$ and $\tilde{v}=\frac{1}{10}$.

Figure 2

(Color online) Largest cluster mass ${\overline{s}}_{max}$ versus the system size.

Figure 3

(Color online) Order-parameter fluctuations plotted versus the system size $L$.

Figure 4

(Color online) EIC data for Binder cumulant $U_4\left(L\right)$ versus $1/L$.

Figure 5

(Color online) Data for $p_c\left(L\right)$ versus $1/L$. Dotted lines describe three-parameter fits and crosses denote exact or best known values.

Figure 6

(Color online) Logarithmic derivative of magnetization $\frac{\partial \text{ln}m}{\partial \beta }$ plotted versus the system size.

Figure 7

(Color online) Distributions $w\left(p_{\left\{\sigma \right\}}\right)$ of $p_{\left\{\sigma \right\}}$ produced by EIC algorithm for the 3D Potts model in the case of strong $\left(q=5\right)$ and weak $\left(q=3\right)$ first-order phase transition.

Figure 8

(Color online) Magnetic autocorrelation function ${\Gamma }_m\left(t\right)$ for EIC, SW, and IC algorithms for 2D, $q=3$. On the inset of the figure are shown the integrated autocorrelation functions for the same cases.

Figure 9

(Color online) Energy autocorrelation functions ${\Gamma }_e\left(t\right)$ of $q=3$, 2D case for several lattice sizes in the exponential region. Dashed lines represent best fits.

Figure 10

(Color online) Integrals of magnetization autocorrelation functions $I_m\left(t_k\right)={\sum }_{t_k}^{t_j=0}{\Gamma }_m\left(t_j\right)$ of 3D Ising for several lattice sizes.

Figure 11

(Color online) Characteristic times of energy and magnetization autocorrelation functions for the systems considered, determined by two approaches described in the text.

Figure 12

(Color online) Behavior of the autocorrelation functions of magnetization for $t_i$ around $N_a=100$ (indicated by the vertical line) in the two cases considered and for various lattice sizes.

Figure 13

(Color online) Autocorrelation functions of magnetization in the case 2D, $q=3$ for different values of $N_a$.