  We investigate some implications of the freezing scenario proposed by
Carpentier and Le Doussal (CLD) for a random energy model (REM) with
logarithmically correlated random potential. We introduce a particular
(circular) variant of the model, and show that the integer moments of the
partition function in the high-temperature phase are given by the well-known
Dyson Coulomb gas integrals. The CLD freezing scenario allows one to use those
moments for extracting the distribution of the free energy in both high- and
low-temperature phases. In particular, it yields the full distribution of the
minimal value in the potential sequence. This provides an explicit new class of
extreme-value statistics for strongly correlated variables, manifestly
different from the standard Gumbel class.
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