Equilibriumlike extension of the invaded cluster algorithm

We propose an extension of the nonequilibrium invaded cluster (IC) algorithm, which reestablishes a correct scaling of fluctuations at criticality and also self-adjusts to the critical temperature. We show that by introducing a single constraint to the intrinsic quantity of the IC algorithm the temperature becomes well defined and the sampling of the equilibrium ensemble is regained. The procedure is applied to the Potts model in two and three dimensions.

Figure 1

(Color online) Energy histograms $w\left(e\right)$ of the EIC, SW, and IC algorithm for the 3D Ising model and sizes $L=16$ and $L=36$ rescaled with the same exponent $x\approx 1.34$. $\overline{e}$ denotes the averaged energy of each individual curve. Histograms of the SW algorithm were taken at $p_c\left(L\right){\mid }_{EIC}$.

Figure 2

(Color online) Data of $p_c\left(L\right)$ for cases $D=2$, $q=2,3$ and $D=3$, $q=2$. Lines represent linear fits, using exact or best known results for $\frac{1}{\nu }$.

Figure 3

(Color online) A log-log plot of the fluctuations of magnetization depending on the system size $L$.