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The O(n) vector model with logarithmic action on a lattice of coordination 3is related to a gas of self-avoiding loops on the lattice. This formulationallows for analytical continuation in n: critical behaviour is found in thereal interval [-2,2]. The solution of the model on random planar lattices,recovered by random matrices, also involves an analytic continuation in thenumber n of auxiliary matrices. Here we show that, in the two cases n=-1, -2, acombinatorial reformulation of the loop gas problem allows to achieve therandom matrix solution with no need of this analytical continuation.Comment: 4 pages, 2 figure

The fractality of sea-ice drift dynamics as revealed from the ‘North Pole 32’ monitoring