Several computer simulations studying a variety of topics in statistical mechanics and lattice gauge theories are performed. / The first study describes a Monte Carlo simulation performed on Ising systems defined on Sierpinsky carpets of dimension between one and four. The critical coupling and the exponent $\gamma$ are measured as a function of dimension. The conclusions drawn from the study are that fractals of the Sierpinsky carpet type can be used to extrapolate statistical systems smoothly between integer dimension in the way given by the $\epsilon$-expansion. The Ising gauge theory in $d = 4 -\epsilon,$ for $\epsilon\to 0\sp+,$ is then studied by performing a Monte Carlo simulation for the theory defined on fractals. The study indicates that the first order phase transition of the $d = 4$ theory becomes second order for all $\epsilon\not= 0,$ implying that 4 may be identified as an upper critical dimension for abelian gauge theories. / A high statistics Monte Carlo simulation for the three-dimensional Ising model is presented for lattices of sizes $8\sp3$ to $44\sp3.$ All the data obtained agrees completely, within statistical errors, with the forms predicted by finite-size scaling. The simulations were made possible by developing a very high speed implementation of the Metropolis algorithm. A finite-size scaling study of the susceptibility at criticality gives ${\gamma\over\nu} = 1.964(3).$ / Finally, a method to estimate numerically the partition function of statistical systems is developed. The method is first applied to calculate the partition function of the three dimensional Ising model on lattices of size $5\sp3$ to $10\sp3.$ From a finite-size scaling of the zeros of these partition functions in the complex $\beta$ plane, the estimate $\nu = 0.6295(10)$ is obtained. A study done for the $Z(2)$ and $Z(8)$ gauge theories shows how one can obtain the order of the phase transition from the scaling of the zeros. The method is finally applied to the $SU(2)$ gauge theory. A line of zeros signaling the $g\sbsp{0}{2} = 0$ fixed point is observed. The study also shows that the lines of zeros of even a $2\sp4$ lattice are a qualitative signal to distinguish a potential phase transition from a crossover. / Source: Dissertation Abstracts International, Volume: 48-07, Section: B, page: 2008. / Thesis (Ph.D.)--The Florida State University, 1987.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_76149 |
| Contributors | SALVADOR, ROMAN SALA., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 115 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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