Cluster scaling in the dilute Ising model

Michael Hennecke, U. Heyken

S. V. Semkin, Виктор Павлович Смагин

H.G. Ballesteros, L.A. Fernández, Víctor Martín-Mayor +3 more

H.G. Ballesteros, L.A. Fernández, V. Martín-Mayor +3 more

Yusuke Tomita, Yutaka Okabe

Using the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since we can tune the critical point of each random sample automatically with the PCC algorithm, we succeed in studying the sample-dependent T(c)(L) and the sample average of physical quantities at each T(c)(L) systematically. Using the finite-size scaling (FSS) analysis for T(c)(L), we discuss the importance of corrections to FSS both in the strong-dilution and weak-dilution regions. The critical phenomena of the 2D site-diluted Ising model are shown to be controlled by the pure fixed point. The crossover from the percolation fixed point to the pure Ising fixed point with the system size is explicitly demonstrated by the study of the Binder parameter. We also study the distribution of critical temperature T(c)(L). Its variance shows the power-law L dependence, L(-n), and the estimate of the exponent n is consistent with the prediction of Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996)]. Calculating the relative variance of critical magnetization at the sample-dependent T(c)(L), we show that the 2D site-diluted Ising model exhibits weak self-averaging.

Robin B. Stinchcombe

An extract scaling of the diluted zero temperature transverse Ising chain is used to obtain its exact quantum critical behaviour. The extension, by an approximate cluster method, of the approach to the diluted two-dimensional zero temperature transverse Ising model yields a discontinuity at the percolation concentration in the dependence of critical field on concentration, as conjectured by Harris (1974).