2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/24245Motivated by recent experiments, we compare the Tonks (i.e. hard-core boson gas) regime achieved in an optical lattice with the Tonks regime of a one-dimensional Bose gas in the continuum. For the lattice gas, we compute the local (i.e. on-site) two-body correlations as a function of temperature and the filling of the lattice. It is found that this function saturates to a constant value with increasing temperature. Furthermore, the parameter that characterizes the long-distance correlations in the lattice Tonks regime is also obtained, showing that on the lattice the long-distance correlations enter the Tonks regime more rapidly than in the continuum.4 pages + 1 EPS figure; v2: presentation improved (results and conclusions unchanged), references added, corrected typoMesoscale and Nanoscale Physicstext