Analytic form of a two-dimensional critical distribution

Advanced search
Browse by:

Department | Year

UCL Theses | Latest

Deposit your research

Analytic form of a two-dimensional critical distribution

Bramwell, Steven T; (2022) Analytic form of a two-dimensional critical distribution. Physical Review E , 105 (3) , Article 034142. 10.1103/PhysRevE.105.034142. Green open access

Preview

Text
Bramwell_ Analytic Form of a Two-Dimensional Critical Distribution_VoR.pdf
Download (423kB) | Preview

Abstract

This paper explores the possibility of establishing an analytic form of the distribution of the order parameter fluctuations in a two-dimensional critical spin-wave model, or width fluctuations of a two-dimensional Edwards-Wilkinson interface. It is shown that the characteristic function of the distribution can be expressed exactly as a gamma function quotient, while a Charlier series, using the convolution of two Gumbel distributions as the kernel, converges to the exact result over a restricted domain. These results can also be extended to calculate the temperature dependence of the distribution and give an insight into the origin of Gumbel-like distributions in steady-state and equilibrium quantities that are not extreme values.

Type:	Article
Title:	Analytic form of a two-dimensional critical distribution
Open access status:	An open access version is available from UCL Discovery
DOI:	10.1103/PhysRevE.105.034142
Publisher version:	https://doi.org/10.1103/PhysRevE.105.034142
Language:	English
Additional information:	This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.
UCL classification:	UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy UCL > Provost and Vice Provost Offices > UCL BEAMS UCL
URI:	https://discovery.ucl.ac.uk/id/eprint/10146478