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

Abstract

We introduce a simple nearest-neighbor spin model with multiple metastable phases, the number and decay pathways of which are explicitly controlled by the parameters of the system. With this model we can construct, for example, a system which evolves through an arbitrarily long succession of metastable phases. We also construct systems in which different phases may nucleate competitively from a single initial phase. For such a system, we present a general method to extract from numerical simulations the individual nucleation rates of the nucleating phases. The results show that the Ostwald rule, which predicts which phase will nucleate, must be modified probabilistically when the new phases are almost equally stable. Finally, we show that the nucleation rate of a phase depends, among other things, on the number of other phases accessible from it.

4 pages, 5 figures. Version with one higher-quality figure available at http://www.fis.unam.mx/~dsanders/publications.html v2: Corrected labels on inset of figure 3. v3: Corrected link

References in corpus (11)

• Sampling rare switching events in biochemical networks
• Simulating rare events in equilibrium or non-equilibrium stochastic systems
• Metastable lifetimes in a kinetic Ising model: Dependence on field and system size
• Theoretical evidence for a dense fluid precursor to crystallization
• Monte Carlo with Absorbing Markov Chains: Fast Local Algorithms for Slow Dynamics
• Metastable states in glassy systems
• Multiple phases in stochastic dynamics: geometry and probabilities
• Metastability and Nucleation for the Blume-Capel Model. Different mechanisms of transition
• Statics, metastable states and barriers in protein folding: A replica variational approach
• Formation of a metastable phase due to the presence of impurities
• Metastability in Markov processes

Cited by in corpus (11)

• Forward Flux Sampling for rare event simulations
• The Statistical Mechanics of Dynamic Pathways to Self-assembly
• Studying Rare Events using Forward-Flux Sampling: Recent Breakthroughs and Future Outlook
• Limit of validity of Ostwald's rule of stages in a statistical mechanical model of crystallization
• Competitive nucleation in reversible Probabilistic Cellular Automata
• Freezing of soft-core bosons at zero temperature: A variational theory
• A note on the nucleation with multiple steps: Parallel and series nucleation
• How many phases nucleate in the bidimensional Potts model?
• Nucleation for one-dimensional long-range Ising models
• Multinucleation in the first-order phase transition of the 2d Potts model
• Competitive Heterogeneous Nucleation onto a Microscopic Impurity in a Potts Model