Temperature-Dependent Growth of Fractal and Compact Domains

Recent studies1,2 of physical systems exhibiting fractal growth patterns have made it clear that the fractal morphology is usually a consequence of a non-equilibrium condition which is introduced either as an intrinsic irreversibility, an effective zero-temperature condition, or simply as a constraint in observation time. By lifting the non-equilibrium condition, one will observe restructuring and compact growth3-6 of the system which eventually, in thermodynamic equilibrium, will have a compact morphology. A proper study of the crossover from non-equilibrium fractal growth to equilibrium compact growth requires a temperature as well as a relaxation mechanism. The way to meet these requirements is to introduce a Hamiltonian which governs a spontaneous thermally driven ordering process and which controls the full scenario from nucleation, fractal growth and coarsening of ordered domains, to equilibrium compact growth of the domains.