Numerical transfer-matrix study of a model with competing metastable states

Abstract

phase I`<x|Imf¤|, even in cases where two metastable states compete. The that supports the proportionality relation for the decay rate of the metastable density. This transfer-matrix approach gives a free-energy cost of nucleation behavior in agreement with the analytically continued metastable free-energy particular eigenvectors of the transfer matrix, the fa exhibit finite-range scaling model to obtain complex-valued "constrained" free-energy densities fu. The Blume-Capel model, a three-state lattice-gas model capable of [27] and agrees well with field-theoretical droplet-model calculations [1,3,4,5,28,29]. OCR Output free-energy density is consistent with Monte-Carlo estimates of the metastable lifetime also using the CTM method [25, 26], found that the imaginary part of the constrained Recent studies of the two-dimensional Ising model with nearest-neighbor interactions, the constrained free-energy density and the analytically continued free-energy density. particular, strong quantitative agreement was found between the imaginary part of parts have been demonstrated to be related to the metastable decay rate [24]. In produces a set of "constra.ined" free-energy densities fu, some of whose imaginary model [23], with a constrained-transfer-matrix (CTM) forma.lism. This method state model with weak, long-range forces, the quasi-one-dimensional Ising (QIDI) Rikvold ct al., [20, 21,22] nucleation has been the focus of numerous works. (For reviews, see e. g. Refs. studyThe investigation of metastable states and their decay through thermally activated

Competitive nucleation and the Ostwald rule in a generalized Potts model with multiple metastable phases

“…A three-phase succession was previously observed in a kinetic Blume-Capel model, 19,20 corresponding to a special case of our model with q =3. 21 The physical reason for the observed transitions is, however, much more transparent with the Hamiltonian in the form ͑1͒, with its intuitive interpretation in terms of attractive and repulsive interactions.…”

Method to study relaxation of metastable phases: Macroscopic mean-field dynamics

“…The application of such ideas to a fieldtheoretical droplet model with Fokker-Planck dynamics has shown that close to coexistence, the nucleation rate for droplets of the equilibrium phase is proportional to the imaginary part of a complex-valued constrained free energy obtained by analytic continuation from the equilibrium phase into the metastable phase [8][9][10]. long-range forces [13][14][15] by a constrained-transfer-matrix method introduced by one of us [16]. Although no dynamical aspects were explicitly considered to obtain the constrained free energies, the average free-energy cost of a critical droplet was obtained over a wide range of fields and temperatures, in good agreement with the predictions of field-theoretical droplet models [8][9][10]14,15,17] and Monte Carlo (MC) simulations [1,[4][5][6].…”

“…long-range forces [13][14][15] by a constrained-transfer-matrix method introduced by one of us [16]. Although no dynamical aspects were explicitly considered to obtain the constrained free energies, the average free-energy cost of a critical droplet was obtained over a wide range of fields and temperatures, in good agreement with the predictions of field-theoretical droplet models [8][9][10]14,15,17] and Monte Carlo (MC) simulations [1,[4][5][6]. These results indicate the relevance of purely static properties, such as the free energy, to the relaxation behavior of metastable phases.…”

Competitive nucleation in reversible probabilistic cellular automata

“…It is then of interest the study of models in which a complete control of the variations induced on the energy landscape by changes in the parameters is possible.In this perspective, the analysis of the Blume-Capel model in Ref. [12,13] and that of the Potts model in Ref.[14] are of great interest. In the Blume-Capel model the sites of the lattice can be either empty or occupied by a 1/2-spin particle.…”