When is a one-dimensional lattice small?

While the use of continuum approximations to describe systems consisting of many molecules is well established, it is not known how such approximation s fail as the number of molecular components decreases. We study the one-di mensional Fermi-Pasta-Ulam chain in order to determine the critical Value o f the system size below which the system's behavior deviates from the conti nuum limit, allowing us to delineate between "small" and "large" systems an d define these terms precisely. For this system, the distinction between sm all and large is correlated with the appearance of an instability of the ch ain.