Monte Carlo physics: a cautionary lesson.

To simulate chance occurrences, a computer can't literally toss a coin or roll a die. Instead, it relies on special numerical recipes for generating strings of shuffled digits that pass for random numbers. Such sequences of pseudorandom numbers play crucial roles not only in computer games but also in simulations of physical processes.

Researchers have long known that the use of particular methods for generating random numbers can produce misleading results in simulations. Now Alan M. Ferrenberg, a computational physicist at the University of Georgia in Athens, and his co-workers have discovered that even "high-quality" random-number generators, which pass a battery of randomness tests, can yield incorrect results under certain circumstances.

The researchers report the findings in the Dec. 7 PHYSICAL REVIEW LETTERS.

Initially, the approach taken by Ferrenberg and his co-workers looked promising. They were interested in simulating the so-called Ising model, which features an abrupt, temperature-dependent transition from an ordered to a disordered state in a system in which neighboring particles have either the same or opposite spins.

To accomplish this goal, they selected a spin-flipping algorithm recently developed by Ulli Wolff of the University of Kiel in Germany and the new "subtract-with-borrow" random-number generator of George Marsaglia and Arif Zaman of Florida State University in Tallahassee (SN: 11/9/91, p. 300). In preparation for simulating the three-dimensional Ising model, Ferrenberg tested this package on the two-dimensional version, which has a known answer. "I got the wrong result:' Ferrenberg says.

Believing that the problem lay in how he had written his computer program, Ferrenberg spent three weeks looking for errors, but he found none. "As far as we could tell, we had exhausted every possibility -- except the random-number generator," he remarks.

As a last resort, Ferrenberg substituted different random-number generators and, to his surprise, found that he came much closer to the correct answer by using a linear congruential generator, which has known defects.

"What we got out of this was that some random-number generators will work with one simulation algorithm and not with others:' Ferrenberg says. "It's very discouraging."

"I am not at all surprised at the kind of results observed;' comments J.A. Reeds of AT&T Bell Laboratories in Murray Hill, N.J. Reeds had encountered a similar problem with the Marsaglia-Zaman random-number generators in a different type of computation.

In an additional twist on the curious behavior of random-number generators, Shu Tezuka of the IBM Tokyo Research Laboratory in Japan and Pierre L'Ecuyer of the University of Montreal in Quebec have now proved that the Marsaglia-Zaman random-number generators are "essentially equivalent" to linear congruential methods. Therefore, these generators share many of the same characteristics and faults.

L'Ecuyer presented this analysis at this week's Winter Simulation Conference, held in Arlington, Va.

The uncertainty about how subtle, hidden patterns among digits spewed out by various random-number generators may influence simulation results presents researchers using so-called Monte Carlo methods with a serious dilemma, especially when the answer is not known.

"Since there is no reason to believe that the model which we have investigated has any special idiosyncrasies, these results offer another stern warning about the need to very carefully test the implementation of new algorithms:' Ferrenberg and his co-workers conclude. "In particular, this means that a specific algorithm must be tested together with the random-number generator being used regardless of the tests which the generator has passed."