We compute the two-point correlation function for spin configurations which
are obtained by solving the Euclidean matching problem, for one family of
points on a grid, and the second family chosen uniformly at random, when the
cost depends on a power p of the Euclidean distance. We provide the analytic
solution in the thermodynamic limit, in a number of cases (p>1 open b.c.\ and
p=2 periodic b.c., both at criticality), and analyse numerically other parts
of the phase diagram.Comment: 34 pages, 10 figure