Comparative study of an Eden model for the irreversible growth of spins and the equilibrium Ising model - art. no. 066127

The magnetic Eden model (MEM) [N. Vandewalle and M. Ausloos, Phys. Rev. E 5 0, R635 (1994)] with Ferromagnetic interactions between nearest-neighbor sp ins is studied in (d+1)-dimensional rectangular geometries for d=1,2. In th e MEM, magnetic clusters are grown by adding spins at the boundaries of the clusters. The orientation of the added spins depends on both the energetic interaction with already deposited spins and the temperature, through a Bo ltzmann factor. A numerical Monte Carlo investigation of the MEM has been p erformed and the results of the simulations have been analyzed using finite -size scaling arguments. Rs in the case of the Ising model, the MEM in d = 1 is noncritical (only exhibits an ordered phase at T = 0). In d = 2 the ME M exhibits an order-disorder transition of second order at a finite tempera ture. Such transition has been characterized in detail and the relevant cri tical exponents have been determined. These exponents: are in agreement (wi thin error bars) with those of the Ising model in two dimensions. Further s imilarities between both models have been found by evaluating the probabili ty distribution of the order parameter, the magnetization, and the suscepti bility. Results obtained by means of extensive computer simulations allow u s to put forward a conjecture that establishes a nontrivial correspondence between the MEM for the irreversible growth of spins and the equilibrium is ing model. This conjecture is certainly a theoretical challenge and its con firmation will contribute to the development of a framework for the study o f irreversible growth processes.