Temperature dependent fluctuations in the two-dimensional XY model
| dc.creator | Banks, S. T. | |
| dc.creator | Bramwell, S. T. | |
| dc.date | 2005-07-18 | |
| dc.date.accessioned | 2026-07-07T03:06:02Z | |
| dc.date.available | 2026-07-07T03:06:02Z | |
| dc.description | We present a detailed investigation of the probability density function (PDF) of order parameter fluctuations in the finite two-dimensional XY (2dXY) model. In the low temperature critical phase of this model, the PDF approaches a universal non-Gaussian limit distribution in the limit T-->0. Our analysis resolves the question of temperature dependence of the PDF in this regime, for which conflicting results have been reported. We show analytically that a weak temperature dependence results from the inclusion of multiple loop graphs in a previously-derived graphical expansion. This is confirmed by numerical simulations on two controlled approximations to the 2dXY model: the Harmonic and ``Harmonic XY'' models. The Harmonic model has no Kosterlitz-Thouless-Berezinskii (KTB) transition and the PDF becomes progressively less skewed with increasing temperature until it closely approximates a Gaussian function above T ~ 4π. Near to that temperature we find some evidence of a phase transition, although our observations appear to exclude a thermodynamic singularity. | |
| dc.description | 15 pages, 5 figures and 1 table | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0507424 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0507424 | |
| dc.identifier | J. Phys. A: Math. Gen. 38, 5603 (2005) | |
| dc.identifier | doi:10.1088/0305-4470/38/25/001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/26667 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Temperature dependent fluctuations in the two-dimensional XY model | |
| dc.type | text |