  Motivated by the possibility to load multi-color fermionic atoms in optical
lattices, we study the entropy dependence of the properties of the
one-dimensional antiferromagnetic SU(N) Heisenberg model, the effective model
of the SU(N) Hubbard model with one particle per site (filling 1/N). Using
continuous-time world line Monte Carlo simulations for N=2 to 5, we show that
characteristic short-range correlations develop at low temperature as a
precursor of the ground state algebraic correlations. We also calculate the
entropy as a function of temperature, and we show that the first sign of
short-range order appears at an entropy per particle that increases with N and
already reaches 0.8k_B at N=4, in the range of experimentally accessible
values.
