2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97989We demonstrate that the ``worm'' algorithm allows very effective and precise quantum Monte Carlo (QMC) simulations of spin systems in a magnetic field, and its auto-correlation time is rather insensitive to the value of H at low temperature. Magnetization curves for the $s=1/2$ and $s=1$ chains are presented and compared with existing Bethe ansatz and exact diagonalization results. From the Green function analysis we deduce the magnon spectra in the s=1 system, and directly establish the "relativistic" form E(p)=(Δ^2 +v^2 p^2)^{1/2} of the dispersion law.6 pages, 8 figures; removed discussion of spin-2 case - will be published later in a separate paperStrongly Correlated ElectronsStatistical Mechanicstext