Transfer-matrix and finite-size scaling methods are applied to two different lattice-gas models to elucidate equilibrium and nonequilibrium aspects of first-order phase transitions in systems with interactions of finite range. / The first model is derived from the anisotropic (asymmetric) next-nearest-neighbor interaction (ASYNNNI) lattice-gas model which describes the structural phase transitions of the high-temperature superconductor YBa$\sb2$Cu$\sb3$0$\sb{6 + x}$ in terms of second-order phase transitions in the CuO basal planes. To account for experiments indicating that these transitions might be first-order at low temperatures, we extend the ASYNNNI model to include weak attractive anisotropic interactions between next-nearest-neighbor oxygen chains. Using the conventional transfer-matrix method and finite-size scaling, we calculate the equilibrium phase diagram and find first-order phase transitions and tricritical points at low temperatures for the order-order as well as the order-disorder transitions. / The second model is the two-dimensional square-lattice nearest-neighbor Ising ferromagnet. We study the metastability displayed by this model below its critical temperature and in an external field. Applying a constrained-transfer-matrix formalism, we obtain complex-valued constrained free energies. In particular, we study the imaginary part of the constrained free-energy branch that corresponds to the metastable phase. Although droplets are not introduced explicitly, the metastable free energy is obtained in excellent agreement with field-theoretical droplet-model predictions. The finite-size scaling properties are different in the weak-field and intermediate-field regimes, and we identify the corresponding different critical-droplet shapes. Our results extend the region of validity for known results of the field-theoretical droplet model, and they indicate that this transfer-matrix approach provides a nonperturbative numerical continuation of the equilibrium free energy into the metastable phase. / Source: Dissertation Abstracts International, Volume: 55-11, Section: B, page: 4917. / Major Professor: P. A. Rikvold. / Thesis (Ph.D.)--The Florida State University, 1994.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_77297 |
| Contributors | Gunther, Christoph C. A., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 156 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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