Relevance of soft modes for order parameter fluctuations in the Two-Dimensional XY model

Details Relevance of soft modes for order parameter fluctuations in the Two-Dimensional XY model Relevance of soft modes for order parameter fluctuations in the Two-Dimensional XY model

2001-06-11

arxiv.org/abs/cond-mat/0106203v1

Physics

Condensed Matter

Statistical Mechanics

12 pages, 9 figures

Scientific paper

10.1088/0305-4470/35/5/307

We analyse the spin wave approximation for the 2D-XY model, directly in reciprocal space. In this limit the model is diagonal and the normal modes are statistically independent. Despite this simplicity non-trivial critical properties are observed and exploited. We confirm that the observed asymmetry for the probability density function for order parameter fluctuations comes from the divergence of the mode amplitudes across the Brillouin zone. We show that the asymmetry is a many body effect despite the importance played by the zone centre. The precise form of the function is dependent on the details of the Gibbs measure, giving weight to the idea that an effective Gibbs measure should exist in non-equilibrium systems, if a similar distribution is observed.

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