The collapse transition of self-avoiding walks on a square lattice: A computer simulation study

Employing the scanning simulation method, we study the tricritical behavior (at the Flory θ point) of self-avoiding walks with nearest-neighbors attraction energy ε(−‖ε‖) on a square lattice. We obtain −ε/kBTt=0.658±0.004, where Tt is the tricritical temperature and kB is the Boltzmann constant. The radius of gyration G and the end-to-end distance R lead to νt(G)=0.5795±0.0030 and νt(R) =0.574±0.006, respectively. We also obtain γt=1.11±0.022 and μt =3.213±0.013, where γt is the free energy exponent and μt is the growth parameter. Three estimates are calculated for the crossover exponent φt , based, respectively, on G, R and the specific heat C: φt (G)=0.597±0.008, φt(R)=0.564±0.009, and φt(C)=0.66±0.02. Our values for νt and γt are close to the Duplantier and Saleur exact values for the θ′ point, νt =4/7=0.571... and γt=8/7=1.142 ... . However, our values of φt are significantly larger than the exact value φt=3/7=0.42... . This suggests that the θ and θ′ points belong to different universality classes.