The collapse transition of selfavoiding 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 selfavoiding walks with nearestneighbors attraction energy ∊(‖∊‖) on a square lattice. We obtain ∊/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 endtoend 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.
 Publication:

Journal of Chemical Physics
 Pub Date:
 August 1989
 DOI:
 10.1063/1.457014
 Bibcode:
 1989JChPh..91.2544M