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Boltzmann-Gibbs measures associated with log-correlated Gaussian fields

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Boltzmann-Gibbs measures associated with log-correlated Gaussian fields possess multifractal properties which are captured by the multifractal exponents. While both the quenched and the annealed multifractal exponents exhibit a phase transition at low temperature known as freezing in the spin glass literature, we show via a convexity argument that the leading-order term of the annealed exponent exhibits another phase transition at some intermediate temperature which may be explained by a partial localisation mechanism similar to freezing. If time permits we discuss a different approach to the problem which allows us to establish a further phase transition in the second order.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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