Spectral Gap Critical Exponent for Glauber Dynamics of Hierarchical Spin Models
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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
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1432-0916