I'll let Thereza take up the 3D issue.  She has done all the 3D running.
We can certainly look at 2D-3D cross-over by increasing the z dimension
as you suggest.  I do not think we have that data right now.  Probably
Thereza's results are all for Lx=Ly=Lz.

It turned out I messed up my script for submitting jobs last night
and the runs pooped out at L=14.  I resubmitted them this morning
and they'll be done in the late afternoon.  Again, those will be 8x8
lattices with dtau=0.125 and U=10.  If we want to be super
careful we will want to check the lattice size and dtau corrections.

Richard Scalettar
Professor and Vice Chairman, Physics Department
University of California, Davis 95616
phone 530-554-1605
fax   530-752-4717
email scalettar@physics.ucdavis.edu
http://leopard.physics.ucdavis.edu/rts/

On Wed, 28 Apr 2010, Nils Bluemer wrote:

Dear Richard,

thank you so much! I have been speculating for a while that our D(T) curves which we propose as an experimental signal for nearest-neighbor AF correlations in cold atoms might be quantitatively accurate, even though the real Neel temperature is much below the DMFT estimate (in 3D). So it is really exciting to see that reasonable quantitative agreement is obtained even in 2 dimensions, where T_N=0.

You can find more information in the preprint that we submitted last night: http://arxiv.org/abs/1004.4857

We do already have some DMFT data obtained directly for the square lattice (which agrees nicely with the rescaled cubic data in the strong coupling range); we will complete it for the full temperature and strong coupling range (U=8,10,12) within the next few days.

If you happened to have also data for nearest-neighbor spin correlations <S_i S_j> we would be very interested. Ultimately, of course, one would also like to directly test the impact of dimensionality by comparing, e.g. 6x6 with 6x6x4 or 8x8 with 8x8x4 (as long as 8^3 or 10^3 appears as too expensive).

Best regards

Nils

On 28.04.2010, at 06:13, <scalettar@physics.ucdavis.edu>
wrote:

Dear Nils,

For now, please look atthe data in Figure 3 of the attached paper
for U=10 and U=12.  This gives the local moment, from which of course you
can extract D via D = (1-m^2)/2.  I will try to find the data, but measuring off the graph with a ruler I see quite close to your
claimed 50% increase in D.  I would say, however, that the smallest
D occurs at a T/t  closer to 0.5 than 0.4.  the value, again just judging
from the graph, seems to be quite close to your 0.025.

A warning is that the data is for 6x6 lattices.  We expect finite size
effects to be small, especially as U increases, but yu can see
what their size is for U=4 in Figure 2.

We'll see what Thereza comes up with.  I may try to do a few runs
on different lattice sizes and with different Trotter step sizes for
U=10 so that we can get a number for you which is corrected both
for finite size error and for the discretization of imaginary time.

Richard Scalettar
Professor and Vice Chairman, Physics Department
University of California, Davis 95616
phone 530-554-1605
fax   530-752-4717
email scalettar@physics.ucdavis.edu
http://leopard.physics.ucdavis.edu/rts/<PRB63_125116_2001.pdf>

Nils Blümer
Institut für Physik, KOMET 337            Room: 03 134, Staudingerweg 7
Johannes Gutenberg-Universität        Phone: (+49) 6131 / 392 22 77
55099 Mainz, Germany                FAX:   (+49) 6131 / 392 09 54
http://komet337.physik.uni-mainz.de/Bluemer/