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arXiv · 2109.13877

Analytic Form of a Two-Dimensional Critical Distribution

Steven T. Bramwell
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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.

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Steven T. Bramwell. 2021-09-28. Analytic Form of a Two-Dimensional Critical Distribution. https://doi.org/10.1103/physreve.105.034142

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