We present a system exhibiting giant proximity effects which parallel observations in superfluid helium (Perron et al, Nature Physics V. 6, 499 (2010)) and give a theoretical explanation of these phenomena based on the mesoscopic picture of phase coexistence in finite systems. Our theory is confirmed by MC simulation studies. Our work demonstrates that such action-at-a-distance can occur in classical systems involving simple or complex fluids, such as colloid-polymer mixtures, or ferromagnets.
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