Exact enumeration of self-avoiding walks on lattices with random site energies

The self-avoiding random walk on lattices with quenched random site energies is studied using exact enumeration in d=2 and 3. For each configuration we compute the size R and energy E of the minimum-energy self-avoiding walk (SAW). Configuration averages yield the exponents ν and χ, defined by ${\mathit{R}}^2$¯∼${\mathit{N}}^{2\nu }$ and δ${\mathit{E}}^2$¯∼${\mathit{N}}^{2\mathrm{\chi }}$. These calculations indicate that ν is significantly larger than its value in the pure system. Finite-temperature studies support the notion that the system is controlled by a zero-temperature fixed point. Consequently, exponents obtained from minimum-energy SAW’s characterize the properties of finite temperature SAW’s on disordered lattices.