Critical behavior of the Baxter-Wu model with quenched impurities

We have used an importance-sampling Monte Carlo technique to study the Baxter-Wu model with various fractions of the lattice sites occupied by random, quenched, nonmagnetic, site impurities. We found the system had long-time fluctuations which were caused by the creation and motion of domain boundaries. For this reason our study required the use of a large number of Monte Carlo steps per spin. The data were analyzed using finite-size scaling to extract the infinite-lattice critical exponents and critical amplitudes from the Monte Carlo simulation of finite lattices. This analysis of the data for the pure Baxter-Wu model yielded results which agreed well with exact results and series-expansion predictions. The addition of quenched site impurities caused a dramatic change in the critical behavior. The pure-lattice critical exponents ($\nu =\frac{2}{3}$, $\alpha =\frac{2}{3}$, ${\gamma }_m\simeq 1.17$) change upon the addition of only a few percent impurities to $\nu =1.00\mathrm{}\pm 0.07$, $\alpha \lesssim 0.0$, and ${\gamma }_m=1.95\mathrm{}\pm 0.08$. The phase diagram as a function of impurity concentration and an estimate for the infinite-lattice percolation limit are also given.