Dear Thereza,
thank you very much, this data is absolutely fantastic for us! Sorry for the late reply, but we could only start the comparisons last Monday and were then a bit carried away with several things we wanted to try.
As you can see in the attached figure, we have at U=6t remarkable agreement between your extrapolated QMC data and our DMFT data in two ways: (i) near-perfect match in D at low T and, even more importantly, (ii) a near-perfect match in the position of the maximum (at T=0.4). Furthermore, there is perfect agreement with DCA at intermediate T.
Thus, I think our paper should be entitled "Signatures of antiferromagnetism at dynamical mean-field critical temperatures in two and three dimensions". I have started writing a PRL draft this week; we plan to send you a version (still in pre-draft form, but with some figures) early next week.
We will definitely not need additional discretizations for the U=6t data that you sent;. In principle we could extend the extrapolation to higher T; however I am certain that we would just reproduce the DCA data. Adding data at lower T is a bit risky (and costly): a significant downward deviation could cause us headaches.
A very important point that we could address with your data is finite-size dependence, using the 6x6x6 versus 8x8x8 data for Delta_tau=0.125. The agreement appears excellent for T>0.3, as you can see in the second figure. Do you think the deviations at the smallest T are significant?
*TODO*: Of course it would be very nice to add more extrapolated QMC data to our comparison. I think that U=4t would be mostful, but only if you can go down to T=1/8. Here, 3 discretization values should be enough, 4 would be plenty. The 8x8x8 data that we have is for Dt=0.125. We should probably also show some extrapolation for U/t=12 for T<=0.5, if not too costly (we have 8x8x8 for Dt=0.0625); e.g. you could use the same for 6x6x6 and add Dt=0.1 and Dt=0.125.
By the way, the gray lines in Figure 1 are fits to the high-temperature parts and correspond to a hypothetical nonmagnetic insulator. We will use them for quantifying the two complementary enhancement effects for D (at strong/weak coupling) at T=0.
Best regards, Nils
PS: Richard, you promised some data for the square lattice. We could use it soon for the draft!
On 15.10.2010, at 19:11, Thereza Cristina de Lacerda Paiva wrote:
Dear Elena and Nils,
I am sending attached two plots that show the dtau dependence of the double occupation for cubic lattices with 6x6x6 size and U=6 at half-filling.
I don´t have the same temperature grid for all dtau values, but there are some Ts for which I gathered 5 dtau values. Graph2 shows the dtau behavior of the double occupation for these Ts. The points are the QMC data and the lines are parabolic fittings. The fittings are really good!
Let me know if you need more dtau values and/or more temperature values.
I´ll send nearest-neighbor spin-spin correlations in a moment.
best,
Thereza
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Thereza Cristina de Lacerda Paiva
Departamento de Fisica dos Solidos
Instituto de Fisica
Universidade Federal do Rio de Janeiro
tclp@if.ufrj.br
www.if.ufrj.br/~tclp/tclp.html
tel: 55 21 2562-7316
fax: 55 21 2562-7368
<doccl6dt01.dat><doccl6dt0125.dat><doccl6dt00833.dat><doccl6dt00625.dat><doccl6dt005.dat><Graph2.eps><Graph1.eps>
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/
