REFEREES: 
theory:
Dr. Krzysztof Byczuk (Warsaw University) Krzysztof.Byczuk@physik.uni-augsburg.de
Dr. Theo Costi (IFF, Juelich) T.Costi@fz-juelich.de
Prof. Eugene Demler (Harvard University) Demler@physics.harvard.edu
Prof. James Freericks (Georgetown University) freericks@physics.georgetown.edu
Prof. Antoines Georges (Ecole Polytechnique) Antoine.Georges@cpht.polytechnique.fr
Prof. Stefan Kehrein (LMU, Munich) Stefan.Kehrein@physik.lmu.de
Dr. Andreas Laeuchli (MPI PKS, Dresden) aml@pks.mpg.de
Prof. Alejandro Muramatsu (Stuttgart University) mu@theo3.physik.uni-stuttgart.de
Prof. Achim Rosch (University of Cologne) rosch@thp.uni-koeln.de
Prof. Jesko Sirker (University of Kaiserslautern) jsirker@physik.uni-kl.de

experiment:
Prof. Immanuel Bloch (MPQ, Munich) immanuel.bloch@mpq.mpg.de
Prof. Tilman Esslinger (ETH Zuerich) esslinger@phys.ethz.ch
Prof. Markus Greiner (Harvard University) greiner@physics.harvard.edu
Prof. Henning Moritz (University of Hamburg) Henning.Moritz@physik.uni-hamburg.de
Prof. Herwig Ott (University of Kaiserslautern) ott@physik.uni-kl.de
Dr. Ulrich Schneider (MPQ, Munich) ulrich.schneider@physik.uni-muenchen.de
Prof. Klaus Sengstock (University of Hamburg) sengstock@physnet.uni-hamburg.de
Prof. Martin Zwierlein (Massachusetts Institute of Technology) ZWIERLEIN@MIT.EDU


NOTES: 
Within the exciting and prominent field of correlated fermions on optical lattices, the experimental search for traces of quantum magnetism is certainly one of the "hot" topics. Current efforts focus on the questions of (i) how cold the experimental systems are currently, (ii) what temperatures are needed for realizing antiferromagnetic (AF) order and (iii) which observables will best show AF signatures. Our paper gives answers to all three questions, with several surprising twists: (a) cooling to half the lowest current entropy is *not* needed, (b) at constant entropy, the short-range physics is hardly dependent on dimensionality, (c) better AF signals can be expected in *lower* dimensions. 

Our results could prove essential for cold-atom experimentalists. However, we know from discussions with renowned experts for magnetism and correlated electron systems that our work teaches important fundamental lessons to this group as well. In particular, our exposition of the counter-intuitive role of dimensionality really worked as an eye-opener. Our work is unique in combining exact results for all relevant dimensions (1;2,3;infinity), which was only possible since the collaboration includes world experts in each of the needed approaches; the resulting insights in the range of applicability of the DMFT will have impact also in material science. 

It should be clear that among the APS journals only Phys. Rev. Lett. is appropriate for this seminal work.

% and in establishing the universal strong-coupling relation between double occupancy and entropy D(s). 

