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arXiv · 1809.02075

Spectral gap critical exponent for Glauber dynamics of hierarchical spin models

Roland Bauerschmidt·Thierry Bodineau
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Abstract

We develop a renormalisation group approach to deriving the asymptotics of the spectral gap of the generator of Glauber type dynamics of spin systems with strong correlations (at and near a critical point). In our approach, we derive a spectral gap inequality for the measure recursively in terms of spectral gap inequalities for a sequence of renormalised measures. We apply our method to hierarchical versions of the $4$-dimensional $n$-component $|\varphi|^4$ model at the critical point and its approach from the high temperature side, and of the $2$-dimensional Sine-Gordon and the Discrete Gaussian models in the rough phase (Kosterlitz--Thouless phase). For these models, we show that the spectral gap decays polynomially like the spectral gap of the dynamics of a free field (with a logarithmic correction for the $|\varphi|^4$ model), the scaling limit of these models in equilibrium.

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Roland Bauerschmidt, Thierry Bodineau. 2018-09-06. Spectral gap critical exponent for Glauber dynamics of hierarchical spin models. https://doi.org/10.1007/s00220-019-03553-x

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