Correlation function for the Grid-Poisson Euclidean matching on a line   and on a circle
  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. 
Elena Boniolo, Sergio Caracciolo, Andrea Sportiello
cond-mat.dis-nn