Some applications of the algorithms

The development over the past decade of efficient Monte Carlo algorithms for the SAW (Section 2.6) has combined with recent advances in computer hardware (notably clusters of high-speed RISC workstations) to make possible high-precision studies of SAWs that would have been unimaginable only a few years ago. For example, a recent study of SAWs nd=2 and J = 3 has employed chain lengths up to iV = 80 000, obtaining error bars of order 0.1-0.3%. (To be sure, this work took several years of CPU time ) 

In this section I cannot hope to do justice to all the applications of the new algorithms. Rather, I shall limit myself to giving an informal account of a few illustrative examples drawn from my own work (most of which is joint work with Sergio Caracciolo, Bin Li, Neal Madras, and Andrea Pelissetto). 

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