Computer simulation study of the θ-point in three dimensions. I. Self-avoiding walks on a simple cubic lattice

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Abstract
Using the scanning simulation method we study the tricritical behavior at the Flory θ-point of self-avoiding walks (SAWs) with nearest neighbors attractions ε (ε<0) on a simple cubic lattice (in the following paper we investigate tricritical trails on the same lattice). The tricritical temperature Tt is −ε/kBTt=0.274±0.006 (one standard deviation). The results for the radius of gyration G and the end-to-end distance R are consistent with the theoretical prediction νt=0.5 and with a logarithmic correction to scaling; the ratio G2/R2 =0.1659±0.0001 (calculated without taking into account correction to scaling) is only slightly smaller than the theoretical asymptotic value 1/6=0.1666.... The results for the partition function Z at Tt lead to γt=1.005±0.017 in accord with theory and to μt=5.058±0.014, where μt is the growth parameter; the correction to scaling in Z is found to be relatively small. For the chain length studied the divergence of the specific heat at Tt (αt≂0.3) is significantly larger than that predicted by theory, (ln N)3/11 (i.e., αt=0). Also, at Tt our data are affected by strong correction to scaling and are thus not consistent with the theoretical value of the crossover exponent φt=0.5.