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 ∊(-‖∊‖) on a square lattice. We obtain -∊/k_BT_t=0.658±0.004, where T_t is the tricritical temperature and k_B is the Boltzmann constant. The radius of gyration G and the end-to-end distance R lead to ν_t(G)=0.5795±0.0030 and ν_t(R) =0.574±0.006, respectively. We also obtain γ_t=1.11±0.022 and μ_t =3.213±0.013, where γ_t is the free energy exponent and μ_t is the growth parameter. Three estimates are calculated for the crossover exponent φ_t, based, respectively, on G, R and the specific heat C: φ_t (G)=0.597±0.008, φ_t(R)=0.564±0.009, and φ_t(C)=0.66±0.02. Our values for ν_t and γ_t are close to the Duplantier and Saleur exact values for the θ' point, ν_t =4/7=0.571... and γ_t=8/7=1.142 ... . However, our values of φ_t are significantly larger than the exact value φ_t=3/7=0.42... . This suggests that the θ and θ' points belong to different universality classes.