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We study the effect of the superconducting gap nodes on the vortex latticeproperties of high temperature superconductors at very low temperatures. Thenonlinear, nonlocal and nonanalytic nature of this effect is shown to havemeasurable consequences for the vortex lattice geometry and the effectivepenetration depth in the mixed state as measured by muon-spin-rotationexperiments.Comment: 3 figures and extensive discussion added, Version to appear in  September 1 issue of PR

Low-temperature behavior of the vortex lattice in unconventional superconductors