Polymer model with annealed dilution on the square lattice: A transfer-matrix study.

Abstract

We study a lattice model for equilibrium polymerization with annealed dilution. The model considered is an Ising lattice-gas monomer-solvent system where the polymers are represented by mutually and self-avoiding walks constrained to pass through sites occupied by monomers. Numerical results on the square lattice using transfer-matrix techniques and finite-size scaling are reported. The values obtained for the tricitical exponent ${\ensuremath{\nu}}_{\mathit{t}}$ are in agreement with the tricritical Ising exponent (8/11) for high values of the monomer fugacity, but the accuracy we obtained does not rule out the possibility of ${\ensuremath{\nu}}_{\mathit{t}}$ being equal to the critical self-avoiding-walk (SAW) value 3/4. Our results indicate that a crossover occurs in the tricritical behavior of the model. This crossover corroborates the equivalence between a particular limit of the diluted model and the self-attracting polymer system proposed recently.