that, in other samples [@DOrtenzio13; @Ross11b] in which the microscopic probes (neutron scattering, $\mu$SR) do not detect LRO, such a partial ordering could occur at the specific heat peak but without ending in a transition at lower temperature. So that the existence of a peak in specific heat may not involve a long-range magnetic ordering. If a LRO transition was also present in the magnetization in these samples, the presence of strong fluctuations might be the clue to explain why the thermodynamic probes (magnetization, specific heat) do show the evidence of a transition while the microscopic ones (neutron scattering, $\mu$SR) do not. Further magnetization measurements would be needed in these samples to answer this question.

Finally, it is interesting to discuss the origin of the transition itself. Theoretical work predicts a first-order character of the transition [@Chang12; @Applegate12; @Savary13], in agreement with the above results. However, the mechanism for the transition is still debated: a Higgs mechanism from a Coulomb phase [@Chang12], or a confinement of the excitations from a thermal spin liquid state [@Savary13] for example have been proposed. It might be of great interest to consider theoretically the effects of the magnetic field on the transition in the 