Analytical and numerical methods are used to study the stationary properties of equilibrium and metastable phases in scalar field theories and model systems with weak, long-range forces (WLRF) by determining the finite-range scaling (FRS) of the free energy F and its analytic continuation $\tilde F$ into the metastable phase. The scaling properties of d-dimensional $\phi\sp n$ scalar field theories are derived, and two special cases are used to study equilibrium and non-equilibrium critical phenomena in WLRF systems. A criterion of critical equivalence is identified, relating the FRS of WLRF systems to the finite-size scaling of hypercylindrical systems above the upper critical dimension. A method of analytically continuing the equilibrium free energy into the metastable phase is generalized for systems exhibiting multiple metastable phases, and new scaling results for $\tilde F$ are found near classical spinodals, including exact results for $d=1.$ An analytic continuation of the free energy is performed numerically on two hypercylindrical systems and compared to analytic expansions for equivalent field theories. Transfer-matrix (TM) finite-size scaling confirms the critical exponents for $d=1$ WLRF systems. For metastable phases, a constrained-transfer-matrix (CTM) method is applied, in which one obtains a "constrained" free-energy density computed directly from the TM. Monte Carlo simulation is performed to obtain decay rates directly, which are compared with both the CTM results and the analytic continuation using Langer's proportionality relation. / Source: Dissertation Abstracts International, Volume: 56-01, Section: B, page: 0316. / Major Professor: Per Arne Rikvold. / Thesis (Ph.D.)--The Florida State University, 1994.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_77347 |
| Contributors | Gorman, Bryan Michael., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 141 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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