The Influence of the Spinodal in Metastable Ising Models.

In this thesis, the influence of the spinodal upon the nucleation process and the quasiequilibrium properties of the metastable state is investigated. The systems which are analyzed are Ising models with both nearest-neighbor and long-range interactions. This work is a continuation of that of Klein and Unger concerning spinodal-assisted nucleation. The structure of the nucleating droplets near the spinodal is studied. These droplets are isomorphic to percolation clusters in a long-range bond percolation problem. Properties of this percolation problem are investigated using computer simulations and scaling arguments. A well -defined region of mean-field behavior is found. The scaling properties of the percolation clusters are investigated and certain aspects of the crossover to d-dimensional percolation are elucidated. These results are then used to investigate nucleating droplets in metastable long-range Ising models. The spinodal-assisted nucleation theory is found to agree well with quantitative measurements of critical exponents from simulation data. The possibility of the existence of spinodal singularities in nearest-neighbor Ising models above six dimensions is studied. Both renormalization group ideas and simulations are used in this work.