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

Abstract

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/k B T 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 heatC: 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.