A new simulation of branched polymers

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Abstract
The scanning method for the simulation of linear chain is extended to general models of branched polymers without loops. A branched chain grows in 'time' (namely, a number of steps from the origin). Therefore (i) in contrast to other simulation techniques, which are of a relaxation type, the chains are statistically independent and the statistical error can reliably be estimated, (ii) the probability of a chain is known and hence the entropy, and (iii) the scanning construction enables one to study geometrical properties which depend on time. For self-avoiding trees on a square lattice, the author obtains the relatively accurate estimates for the static critical exponents, nu =0.640+or-0.004 and theta =1.003+or-0.02 and for the connective constant mu =5.1419+or-0.003. The author also obtains critical exponents gamma t approximately=1.26 and nu t approximately=0.83, which characterise the growth in time of the number of bonds and the gyration radius respectively. Application of the scanning method to more complex branched polymers is discussed.