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We report about extensive Monte Carlo simulations of disordered Ising systems with concentrations of magnetic sites between p = 1.0 and p=O.5. We have measured the magnetization, the susceptibility and the caloric properties in the critical region. In addition the magnetization-energy correlation function has been investigated and the critical exponent C = 1 -, B = (a + y)/2 has been determined. We fmd that power law behaviour and scaling is fulfilled in the whole concentration range. The effective critical exponents y, , B and C are shown to be concentration dependent. In the range of strong disorder y and , B increase until they reach a kind of asymptotic behaviour at , I 3 = 0.335f 0.01 and y = 1.49 k 0.02 for p = 0.5. In accord with the exponent relation C=l-P the critical exponent < decreases with dilution to Z: = 0.675 f 0.01.Monte Carlo simulation of strongly diluted Ising ferromagnets. -In this paper we report about Monte Carlo simulations of the site diluted Ising model in three dimensions. This is the simplest physical system where the influence of disorder on the critical behaviour can be studied. We have performed simulations in a large concentration range between the pure system ( p = 1.0) and the percolation concentration (p,=O.31) of the simple cubic Ising system. Thus, we have observed the weakly disordered regime where most of the analytical works[1-5] should be applicable as well as the strongly disordered regime where the influence of percolation becomes important [69]. The most important conjecture concerning the critical behaviour of weakly disordered ferromagnets is the Harris criterion [5] which states that the critical behaviour remains unchanged if the exponent ah of the pure system is negative; for positive ah a new type of critical behaviour should appear. Renormalization group works[1-41 on we@y diluted systems have confirmed this conjecture. Since the crossover exponent with respect to disorder q $ ! = ah = 0.11 of Ising systems is extremely small, the critical behaviour is expected to be modified by disorder only very near T, (It1 < ( l -p ) l ' # ~) i.e. It 1 <10-lo for p=O.9). Other works on the critical behaviour of disordered spin systems have started from the opposite extreme, the percolation threshold [6-91. Starting point of these works is the ramified cluster structure on which quasi one-dimensional correlations determine the critical behaviour near T, = 0. It has been * * * It is a pleasure to thank D. STAUFFER and J.-S. WANG for discussions about the determination ,of critical exponents. This work was supported by the Sonderforschungsbereich 237 .Disorder and Large Fluctuations..

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We performed extensive Monte Carlo simulations of site-disordered two-dimensional Ising systems along the critical line T, (p) in the concentration range of magnetic sites between p =0.6 and p =1.0 (p, =0.59). Magnetic and caloric properties were studied as well as the cumulants of the magnetization distribution. We found that the disorder induces a crossover phenomenon in the experimental temperature range which leads to a strong, concentration-dependent increase of y,& (y, "=2.16 for p =0. 7) in the temperature range 10 '&(T -T, )/T, &10'. Near T"y,z asymptotically approaches y=1.75, independent of the concentration. We propose a model of weakly coupled compact clusters of spins to describe this crossover phenomenon.There is a long-standing research interest in critical phenomena in disordered spin systems. The main question is how the disorder changes the nature of the phase transition and thereby the universality class. ' The asymptotic critical behavior may be changed in three different ways: (i) The disorder may be an irrelevant perturbation so that the critical behavior is asymptotically unchanged; (ii) the disorder may be relevant and lead to a different universality class; and (ii) in rare cases, the disorder may lead to critical exponents which depend continuously on the concentration. Heisenberg systems belong to the first category; their crossover exponent P" with respect to disorder is equal to the critical exponent of the specific heat of the pure system aI, = -0.09; thus the disorder is asymptotically irrelevant.In threedimensional Ising systems, the disorder is a relevant perturbation leading to a different universality class: The set critical exponents change from (a =0. 11, P= 0.325, y= 1.24 v=0. 63) to (a= -0.01, P=0.34, y= 1.32, v=0. 67).These results confirm the heuristic Harris criterion:Disorder is relevant, if vt, (2/d, which is equivalent to a& &0 if hyperscaling is valid. The twodimensional Ising system is marginal in this respect since its correlation length diverges with vI, =1 and the specific heat with a&=0, respectively. Recent work based on conformal invariance ' methods have led to predictions for the bond-diluted two-dimensional Ising system:The critical exponents (a=O, P= -, ', y= -, ', v= 1) remain unchanged -disorder leads to logarithmic corrections only; e. g., the susceptibility diverges as y-t~~lnt~~, the magnetization becomes M -t'~~l nt~~' , and the specific heat gets a double-logarithmic form.It must be stated clearly that the validity of all results' ' is restricted in two ways: (i) All approaches are restricted to weak disorder since disorder is treated as a perturbation of the pure system -it is not clear what weak disorder means; (ii) all results are valid asymptotically near the critical point -there is no measure where this asymptotic regime is reached on experimentally accessible concentration and temperature scales. Complementary approaches to critical phenomena in disordered spin systems have started from the opposite limit, i.e. , from the percolation fixed p...