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