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 R²{}{~}N^2ν and {δ}E²{}{~}N^2χ. 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.