Structural instabilities of DLA-like fractals at finite temperatures

Abstract

The stability of DLA-like fractal structures are investigated at finite temperatures. A Peierls instability or "melting" of the fractal occurs at a temperature T_m which decreases with the size (mass M) of the fractal: T_m ≈ M^-(t-1), t=z/d_f, where z is the dynamic exponent, (for diffusive elastic modes on the fractal) and d_f is the fractal dimensionality. A finite temperature Monte Carlo simulation study of the instability indicates z < d_f+1 for such fractals. It is also shown that with suitable combination of harmonic and anharmonic terms a structural transition (phonon-softening) is possible at a temperature independent of the size of the aggregate.