  Open segments of S=1 antiferromagnetic spin chains are studied at finite
temperatures and fields using continuous time Quantum Monte Carlo techniques.
By calculating the resulting magnetization profiles for a large range of chain
lengths with fixed field and temperature we reconstruct the experimentally
measured NMR spectrum of impurity doped Y$_2$BaNi$_{1-x}$Mg$_x$O$_5$. For
temperatures above the gap the calculated NMR spectra are in excellent
agreement with the experimental results, confirming the existence of $S=1/2$
excitations at the end of open S=1 chain segments. At temperatures below the
gap, neglecting inter chain couplings, we still find well defined peaks in the
calculated NMR spectra corresponding to the $S=1/2$ chain end excitations. At
low temperatures, inter chain couplings could be important, resulting in a more
complicated phase.
