  We consider generic finite range percolation models on $\mathbb{Z}^d$ under a
high temperature assumption (exponential decay of connection probabilities and
exponential ratio weak mixing). We prove that the rate of decay of
point-to-point connections exists in every directions and show that it
naturally extends to a norm on $\mathbb{R}^d$. This result is the base input to
obtain fine understanding of the high temperature phase and is usually proven
using correlation inequalities (such as FKG). The present work makes no use of
such model specific properties.
