2026-09-21T02:48:28Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/18883 2023-07-10 col_2142_5131 col_2142_8859 com_2142_5130 com_2142_8858 com_2142_234

Kogut, John B. Scheinine, Alan Louis 2011-04-27T14:20:40Z 2011-04-27T14:20:40Z 10000-01-01 1992 The frustrated XY model was studied on a lattice, primarily to test the Fourier transform acceleration technique for a phase transition having more field structure than just spinwaves and vortices. Also, the spinless Hubbard model without hopping was simulated using continuous variables for the auxiliary field that mediates the coupling between fermions. Finally, the spin one-half Hubbard model was studied with a technique that sampled the fermion occupation configurations. The frustrated two-dimensional XY model was simulated using the Langevin equation with Fourier transform acceleration. The speedup due to Fourier acceleration was measured for frustration one-half at the transition temperature. For comparison, the unfrustrated XY model was also studied. For the frustrated case, only the long-distance spin correlation and the autocorrelation of the spin showed significant speedup. The frustrated case has Isinglike domains. It was found that Fourier acceleration speeds the evolution of spinwaves but has negligible effect on the Ising-like domains. In the Hubbard model, the fermion determinant weight factor in the partition function changes sign, causing large statistical fluctuations of observables. A technique was found for sampling configuration space using continuous auxiliary fields, despite energy barriers where the fermion determinant changes sign. For the two-dimensional spinless Hubbard model with no hopping, an exact solution was found for a 4 x 4 lattice; which could be compared to numerical simulations. The sign problem remained, and was found to be related to the sign problem encountered when a discrete variable is used for the auxiliary field. For the spin one-half Hubbard model, a Monte Carlo simulation was done in which the fermion occupation configurations were varied. Rather than integrate-out the fermions and make a numerical estimate of the sum over the auxiliary field, the auxiliary field was integrated-out and a numerical estimate was made of the sum over fermion configurations. Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-04-27T14:20:40Z No. of bitstreams: 1 1992_Scheinine.pdf: 1760462 bytes, checksum: 5190ede06e9d9e2343355b315d49967f (MD5) Made available in DSpace on 2011-04-27T14:20:40Z (GMT). No. of bitstreams: 1 1992_Scheinine.pdf: 1760462 bytes, checksum: 5190ede06e9d9e2343355b315d49967f (MD5) Previous issue date: 1992 Restriction data tranferred 2014-07-01T11:12:15-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-04-27T14:20:41Z Item is restricted indefinitely. Thesis U of I Only 3488516 http://hdl.handle.net/2142/18883 en 1992 Alan Louis Scheinine frustrated XY model Fourier-accelerated Langevin simulation Hubbard model computational physics Fourier-accelerated Langevin simulation of the frustrated XY model and simulation of the spinless and spin one-half Hubbard model Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.