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arXiv · 1403.1836

Correlation function for the Grid-Poisson Euclidean matching on a line and on a circle

Elena Boniolo·Sergio Caracciolo·Andrea Sportiello
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Abstract

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.

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Elena Boniolo, Sergio Caracciolo, Andrea Sportiello. 2014-03-07. Correlation function for the Grid-Poisson Euclidean matching on a line and on a circle. https://doi.org/10.1088/1742-5468%2F2014%2F11%2Fp11023

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