About two cluster generating algorithms

Two original algorithms used to generate n-element clusters in a rectangular lattice are presented. The first algorithm, suitable for simulations related to thermodynamic investigations of metastable cluster systems [V.A. Shneidman, G.M. Nita, On the critical cluster in the 2-dimensional Ising model: computer-assisted exact results, J. Chem. Phys. 121 (11232) 2004], is able to generate all distinguishable cluster configurations with a given number of elements. The maximum number of elements forming such two dimensional configurations is limited only by the computational time involved, which is shown to be essentially improved by using a parallel processing approach. The complete results up to 17 cluster elements are presented. The second algorithm, suitable for dynamic simulations [V.A. Shneidman, G.M. Nita, Modulation of the nucleation rate preexponential in a low-temperature Ising system, Phys. Rev. Lett. 89 (2002) 025701; Phys. Rev. E, 68 (2003) 021605], is able to generate full or partial nucleation chains up to a maximum cluster size limited by the computational time and the virtual memory available. For illustration purposes, the complete nucleation chains up to a 5 elements and partial nucleation chains up to 13 elements are presented in detail, although complete results up to 10 elements and partial nucleation chains up to 100 elements were successfully produced using this algorithm.