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We construct a N-dimensional Gaussian landscape with multiscale, translationinvariant, logarithmic correlations and investigate the statistical mechanicsof a single particle in this environment. In the limit of high dimension N>>1the free energy of the system in the thermodynamic limit coincides with themost general version of Derrida's Generalized Random Energy Model. Thelow-temperature behaviour depends essentially on the spectrum of length scalesinvolved in the construction of the landscape. We argue that our constructionis in fact valid in any finite spatial dimensions, starting from N=1.

On an explicit construction of Parisi landscapes in finite dimensional Euclidean spaces