Recent Results on the Decay of Metastable Phases

TL;DR

This paper reviews recent theoretical, computational, and numerical advances in understanding the decay of metastable phases in many-particle systems, focusing on nucleation, growth, and metastability in lattice models and fluids.

Contribution

It provides a comprehensive overview of recent developments in the study of metastable decay, including new algorithms and finite-size scaling results for different interaction types.

Findings

Weak-long-range-force models have infinitely long-lived metastable phases in the infinite-range limit.

Metastable phases in short-range-force models eventually decay, with extremely slow rates.

Finite-size effects on metastable lifetimes may be observable experimentally.

Abstract

We review some aspects of current knowledge regarding the decay of metastable phases in many-particle systems. In particular we emphasize recent theoretical and computational developments and numerical results regarding homogeneous nucleation and growth in kinetic Ising and lattice-gas models. An introductory discussion of the droplet theory of homogeneous nucleation is followed by a discussion of Monte Carlo and transfer-matrix methods commonly used for numerical study of metastable decay, including some new algorithms. Next we discuss specific classes of systems. These include a brief discussion of recent progress for fluids, and more exhaustive considerations of ferromagnetic Ising models ({\it i.e.}, attractive lattice-gas models) with weak long-range interactions and with short-range interactions. Whereas weak-long-range-force (WLRF) models have infinitely long-lived metastable phases in the infinite-range limit, metastable phases in short-range-force (SRF) models eventually decay, albeit extremely slowly. Recent results on the finite-size scaling of metastable lifetimes in SRF models are reviewed, and it is pointed out that such effects may be experimentally observable.