Comp-phys-alps-users

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1244 discussions

Problem working out a specific Hamiltonian
by Niraj Ghimire 11 Oct '14

11 Oct '14

Dear alps users/developers, I am trying to study the properties of a system using a Hamiltonian that has terms describing nearest-neighbor and next-nearest-neighbor interactions. I am thinking I can do so by simply using one of the Hamiltonians described in "models.xml" but I don't know how. I went through all the tutorials given on the alps homepage but found no help. I will truly appreciate any help or guidance. Thank you, Niraj

2 2

vt_skip="true" in the lattice definition
by Vladimir Iglovikov 09 Oct '14

09 Oct '14

What does vt_skip="true" mean in the lattice definition?

2 1

Re: [ALPS-users] complexity estimation for the 3D ferromagnetic Heisenberg model
by Menchyshyn Oleh 05 Oct '14

05 Oct '14

Dear Prof. Todo, Thank you very much for your answers and time. ありがとうございます Best regards, Oleh

1 0

Re: [ALPS-users] complexity estimation for the 3D ferromagnetic Heisenberg model
by Menchyshyn Oleh 04 Oct '14

04 Oct '14

Thank you for your answers, I think I understand much more now. I would like to clarify just 2 points: 1) I don't get why should I divide 48 by 3? What do you call a bond? - Is it a $ J_{i,j} ( S^x_i * S^x_j + S^y_i * S^y_j + S^z_i * S^z_j ) = J_{i,j} ((S_i, S_j)) $ ? Here I've denoted a scalar product with the double parentheses - Or is it just an edge in the lattice graph? - For example ...................... <EDGE><SOURCE vertex="1" offset="0 0 0"/><TARGET vertex="2" offset="0 0 0"/></EDGE> <EDGE><SOURCE vertex="1" offset="0 0 0"/><TARGET vertex="4" offset="-1 -1 0"/></EDGE> ...................... where the former is an intracell edge, and the later is an intercell edge. I meant I had the 48 such intra- and intercell edges together. 2) I know about --time-limit option, and the tutorial says: -- gives the time (in seconds) which the program should run before writing a final checkpoint and exiting Can I restart the simulation again and make the ALPS using the obtained output data to proceed further? I know it sounds stupid to interrupt the simulation to restart it later. Otherwise, I would need to talk to sysadmin to change privileges for my account, so my simulations could exceed 48 hours. Best regards, Oleh > Dear Oleh, > > On 2014/10/01, at 21:40, Menchyshyn Oleh <oleh.menchyshyn(a)gmail.com> > wrote: > > So in my case, having the lattice with 16 atoms unit cell and 48 intra > and intercell bonds (coupling constants), > > means I would need to multiply the estimated expected time for some > simple reference model by 48? > > Since there are 3 bonds in a unit in my case, 48/3 = 16 would be the > correct factor to be used. > > > The THERMALIZATION and SWEEPS parameters are chosen to meet the relative > errors set up for observables being measured. > > If we increase the size of the system, namely L=8,12,16,24,..., but > leave the SWEEPS the same, the relative error increases and the accuracy of > simulation drops, aren't they? > > The increase of error bar will be very slow (or sometimes negligible) for > the loop algorithm, > as the autocorrelation time stays O(1) irrespective of the system size. > > > I'm asking that to clarify the issue as the cluster I use limits the > jobs running time to 48 hours. > > > > And is it possible in principle in ALPS to stop the calculation and > restart later as a new process? > > Or in that case when I need to analyse the QMC statistics manually? > > You can use the command line option ??time-limit? to specify the time > after which the program > will write final checkpoints and terminate. The simulation will continue > from the checkpoints when > the program is executed again. > > Please read > http://alps.comp-phys.org/mediawiki/index.php/ALPS_using_the_command_line#C… > for more details. > > Best, > Synge >

2 1

Definition of Structure Factor in ALPS
by Stone, Matthew B. 04 Oct '14

04 Oct '14

ALPS community, How is the structure factor defined in ALPS? For example, this value can be included in results files using the parameters 'MEASURE_STRUCTURE_FACTOR[Structure Factor Sz]' : 'Sz'. I am performing calculations using the exact diagonalization and Lanczos ALPS codes for a 1-d chain system. This returns energy levels and momentum such that one can examine the different excitations as a function of energy and wave-vector. I would like to be able to extract parameters for excitations that would be proportional to what is measured in inelastic neutron scattering measurements. This quantity is called the 'dynamical structure factor' or the 'dynamic spin structure factor' or simply S(q,E). Is the STRUCTURE_FACTOR in ALPS related to this quantity? Or is a sum of the spin-spin correlations more appropriate to use for such a calculation? Thanks, Matthew Stone

2 1

DMRG
by hamid mosadegh 02 Oct '14

02 Oct '14

Dear all It seems that we must put a potential on boundary to obtain the ground state using DMRG. How i can add a term as V/2*(n(1)+n(L)) to fermion model in models.xml Thanks -- H. Mosadeq Shahr-e-Kord University (SKU), Shahr-e-Kord , Iran

3 8

Re: [ALPS-users] complexity estimation for the 3D ferromagnetic Heisenberg model
by Menchyshyn Oleh 02 Oct '14

02 Oct '14

Dear Synge, thank you for your attention. So in my case, having the lattice with 16 atoms unit cell and 48 intra and intercell bonds (coupling constants), means I would need to multiply the estimated expected time for some simple reference model by 48? The THERMALIZATION and SWEEPS parameters are chosen to meet the relative errors set up for observables being measured. If we increase the size of the system, namely L=8,12,16,24,..., but leave the SWEEPS the same, the relative error increases and the accuracy of simulation drops, aren't they? I'm asking that to clarify the issue as the cluster I use limits the jobs running time to 48 hours. And is it possible in principle in ALPS to stop the calculation and restart later as a new process? Or in that case when I need to analyse the QMC statistics manually? > Dear Oleh, > > I think that the default value (SWEEPS = 65536, THERMALIZATION = SWEEPS/8) > should be enough > for rough estimation of the critical temperature of simple models. > > The CPU time of the looper code is asymptotically proportional to the > number of bonds (more precisely, > the sum of coupling constants) and as well as to the inverse temperature. > For example, QMC calculation > of simple cubic S=1/2 ferromagnetic Heisenberg model near the Curie point > (T \sim 0.8) takes about > > 16 sec (for L=8) > 52 sec (for L=12) > 134 sec (for L=16) > 450 sec (for L=24) > 1490 sec (for L=36) > > on my x86 workstation. > > Best, > Synge > > > On 2014/10/01, at 3:40, Menchyshyn Oleh <oleh.menchyshyn(a)gmail.com> wrote: > > > Dear Synge, > > > > thank you for your hints. It works nice. > > I think, it would be useful to update the tutorial on that subject, to > make it more clear, > > that parameter file is not the lattice description one. > > I knew it was the two-dimensional model. I put it on purpose, just as an > example. > > > > Can someone experienced in QMC-loop simulations comment on my bigger > problem, please. > > > > > > Message: 10 > > Date: Mon, 29 Sep 2014 11:03:36 +0900 > > From: Synge Todo <wistaria(a)comp-phys.org> > > To: comp-phys-alps-users(a)lists.phys.ethz.ch > > Subject: Re: [ALPS-users] complexity estimation for the 3D > > ferromagnetic Heisenberg model > > Message-ID: <9E0990A4-3582-45B9-B8C6-F704BE452A27(a)comp-phys.org> > > Content-Type: text/plain; charset=windows-1252 > > > > Dear Oleh, > > > > It seems that your lattice ?p_lat? is not defined in THREE dimensions, > but in TWO dimensions. > > Are you really simulating three-dimensional model? > > > > Best, > > Synge > > > > > > On 2014/09/29, at 5:09, Menchyshyn Oleh <oleh.menchyshyn(a)gmail.com> > wrote: > > > > > Dear ALPS community, > > > > > > I am trying to obtain the critical temperature for the 3D > ferromagnetic Heisenberg model S=1/2 on the cubic lattice with a unit cell > which contains 16 atoms. I have made the QMC "loop" simulations for the > lattice with dimensions L = 8, i.e. 8*8*8 unit cells, also for L=10, and > L=12. > > > But there was just a little bend on the magnetisation curve as a sign > of the phase transition which should occur for the ferromagnetic model for > certain. I know I should use the Binder cumulant and the finite size > scaling to locate the phase transition point correctly. > > > I have enlarged my lattice to L=24, but simulation goes very-very > slowly. As I have limited resources to just tens of cores and I have a > feeling I would need to take L=32(48?) at least I want to ask: > > > > > > Based on your experience what order should be the THERMALIZATION and > SWEEPS parameters? > > > How can I estimate the computational complexity of my problem and the > time it would take? > > > Or maybe, I do anything wrong? > > > > > > A one more technical issue. The tutorial on the ALPS says that > correctness of a lattice definition can be checked with "printgraph" tool. > I used it with a couple definition files but all resulted in: > > > > > > Caught exception: parameter parse error at "<LATTICES> <LATTICEGRAPH > name="p" > > > > > > Just for a reference I put a definition of a lattice I know worked > well with simulation tools, but failed with "printgraph" > > > > > > <LATTICES> > > > <LATTICEGRAPH name="p_lat"> > > > <FINITELATTICE> > > > <LATTICE dimension="2"> > > > <BASIS> <VECTOR>1 0</VECTOR><VECTOR>0 1</VECTOR></BASIS> > > > </LATTICE> > > > <PARAMETER name="L"/> > > > <PARAMETER name="M"/> > > > <EXTENT dimension="1" size="L"/> > > > <EXTENT dimension="2" size="M"/> > > > <BOUNDARY type="periodic"/> > > > </FINITELATTICE> > > > <UNITCELL dimension="2" vertices="6"> > > > <VERTEX id="1"><COORDINATE> 0.6 0.2 </COORDINATE></VERTEX> > > > <VERTEX id="2"><COORDINATE> 0.6 0.6 </COORDINATE></VERTEX> > > > <VERTEX id="3"><COORDINATE> 0.2 0.6 </COORDINATE></VERTEX> > > > <VERTEX id="4"><COORDINATE> 0.2 0.2 </COORDINATE></VERTEX> > > > <VERTEX id="5"><COORDINATE> 0.8 0.4 </COORDINATE></VERTEX> > > > <VERTEX id="6"><COORDINATE> 0.4 0.8 </COORDINATE></VERTEX> > > > <EDGE type="2"><SOURCE vertex="1"/><TARGET vertex="2"/></EDGE> > > > <EDGE type="2"><SOURCE vertex="2"/><TARGET vertex="3"/></EDGE> > > > <EDGE type="2"><SOURCE vertex="3"/><TARGET vertex="4"/></EDGE> > > > <EDGE type="2"><SOURCE vertex="1"/><TARGET vertex="4"/></EDGE> > > > <EDGE type="3"><SOURCE vertex="1"/><TARGET vertex="5"/></EDGE> > > > <EDGE type="3"><SOURCE vertex="2"/><TARGET vertex="6"/></EDGE> > > > <EDGE type="1"><SOURCE vertex="2"/><TARGET vertex="5"/></EDGE> > > > <EDGE type="1"><SOURCE vertex="3"/><TARGET vertex="6"/></EDGE> > > > <EDGE type="3"><SOURCE vertex="3"/><TARGET vertex="5" offset="-1 > 0"/></EDGE> > > > <EDGE type="1"><SOURCE vertex="4"/><TARGET vertex="5" offset="-1 > 0"/></EDGE> > > > <EDGE type="3"><SOURCE vertex="4"/><TARGET vertex="6" offset="0 > -1"/></EDGE> > > > <EDGE type="1"><SOURCE vertex="1"/><TARGET vertex="6" offset="0 > -1"/></EDGE> > > > </UNITCELL> > > > </LATTICEGRAPH> > > > </LATTICES> > > > > > > > > > Best regards, > > > Oleh Menchyshyn >

2 1

Re: [ALPS-users] complexity estimation for the 3D ferromagnetic Heisenberg model
by Menchyshyn Oleh 01 Oct '14

01 Oct '14

Dear Synge, thank you for your hints. It works nice. I think, it would be useful to update the tutorial on that subject, to make it more clear, that parameter file is not the lattice description one. I knew it was the two-dimensional model. I put it on purpose, just as an example. Can someone experienced in QMC-loop simulations comment on my bigger problem, please. > > Message: 10 > Date: Mon, 29 Sep 2014 11:03:36 +0900 > From: Synge Todo <wistaria(a)comp-phys.org> > To: comp-phys-alps-users(a)lists.phys.ethz.ch > Subject: Re: [ALPS-users] complexity estimation for the 3D > ferromagnetic Heisenberg model > Message-ID: <9E0990A4-3582-45B9-B8C6-F704BE452A27(a)comp-phys.org> > Content-Type: text/plain; charset=windows-1252 > > Dear Oleh, > > It seems that your lattice ?p_lat? is not defined in THREE dimensions, but > in TWO dimensions. > Are you really simulating three-dimensional model? > > Best, > Synge > > > On 2014/09/29, at 5:09, Menchyshyn Oleh <oleh.menchyshyn(a)gmail.com> wrote: > > > Dear ALPS community, > > > > I am trying to obtain the critical temperature for the 3D ferromagnetic > Heisenberg model S=1/2 on the cubic lattice with a unit cell which contains > 16 atoms. I have made the QMC "loop" simulations for the lattice with > dimensions L = 8, i.e. 8*8*8 unit cells, also for L=10, and L=12. > > But there was just a little bend on the magnetisation curve as a sign of > the phase transition which should occur for the ferromagnetic model for > certain. I know I should use the Binder cumulant and the finite size > scaling to locate the phase transition point correctly. > > I have enlarged my lattice to L=24, but simulation goes very-very > slowly. As I have limited resources to just tens of cores and I have a > feeling I would need to take L=32(48?) at least I want to ask: > > > > Based on your experience what order should be the THERMALIZATION and > SWEEPS parameters? > > How can I estimate the computational complexity of my problem and the > time it would take? > > Or maybe, I do anything wrong? > > > > A one more technical issue. The tutorial on the ALPS says that > correctness of a lattice definition can be checked with "printgraph" tool. > I used it with a couple definition files but all resulted in: > > > > Caught exception: parameter parse error at "<LATTICES> <LATTICEGRAPH > name="p" > > > > Just for a reference I put a definition of a lattice I know worked well > with simulation tools, but failed with "printgraph" > > > > <LATTICES> > > <LATTICEGRAPH name="p_lat"> > > <FINITELATTICE> > > <LATTICE dimension="2"> > > <BASIS> <VECTOR>1 0</VECTOR><VECTOR>0 1</VECTOR></BASIS> > > </LATTICE> > > <PARAMETER name="L"/> > > <PARAMETER name="M"/> > > <EXTENT dimension="1" size="L"/> > > <EXTENT dimension="2" size="M"/> > > <BOUNDARY type="periodic"/> > > </FINITELATTICE> > > <UNITCELL dimension="2" vertices="6"> > > <VERTEX id="1"><COORDINATE> 0.6 0.2 </COORDINATE></VERTEX> > > <VERTEX id="2"><COORDINATE> 0.6 0.6 </COORDINATE></VERTEX> > > <VERTEX id="3"><COORDINATE> 0.2 0.6 </COORDINATE></VERTEX> > > <VERTEX id="4"><COORDINATE> 0.2 0.2 </COORDINATE></VERTEX> > > <VERTEX id="5"><COORDINATE> 0.8 0.4 </COORDINATE></VERTEX> > > <VERTEX id="6"><COORDINATE> 0.4 0.8 </COORDINATE></VERTEX> > > <EDGE type="2"><SOURCE vertex="1"/><TARGET vertex="2"/></EDGE> > > <EDGE type="2"><SOURCE vertex="2"/><TARGET vertex="3"/></EDGE> > > <EDGE type="2"><SOURCE vertex="3"/><TARGET vertex="4"/></EDGE> > > <EDGE type="2"><SOURCE vertex="1"/><TARGET vertex="4"/></EDGE> > > <EDGE type="3"><SOURCE vertex="1"/><TARGET vertex="5"/></EDGE> > > <EDGE type="3"><SOURCE vertex="2"/><TARGET vertex="6"/></EDGE> > > <EDGE type="1"><SOURCE vertex="2"/><TARGET vertex="5"/></EDGE> > > <EDGE type="1"><SOURCE vertex="3"/><TARGET vertex="6"/></EDGE> > > <EDGE type="3"><SOURCE vertex="3"/><TARGET vertex="5" offset="-1 > 0"/></EDGE> > > <EDGE type="1"><SOURCE vertex="4"/><TARGET vertex="5" offset="-1 > 0"/></EDGE> > > <EDGE type="3"><SOURCE vertex="4"/><TARGET vertex="6" offset="0 > -1"/></EDGE> > > <EDGE type="1"><SOURCE vertex="1"/><TARGET vertex="6" offset="0 > -1"/></EDGE> > > </UNITCELL> > > </LATTICEGRAPH> > > </LATTICES> > > > > > > Best regards, > > Oleh Menchyshyn > > > > ------------------------------ > > Message: 11 > Date: Mon, 29 Sep 2014 11:44:07 +0900 > From: Synge Todo <wistaria(a)comp-phys.org> > To: comp-phys-alps-users(a)lists.phys.ethz.ch > Subject: Re: [ALPS-users] complexity estimation for the 3D > ferromagnetic Heisenberg model > Message-ID: <1DFD019C-D86C-4BB5-8152-974E17F7B366(a)comp-phys.org> > Content-Type: text/plain; charset=windows-1252 > > Dear Oleh, > > As for ?printgraph? tool, you have to specify the name of parameter file > (not lattice file). > Please prepare a parameter file (say, ?parms?) that includes, e.g. > > LATTICE_LIBRARY = "lattice.xml" > LATTICE = "p_lat" > L = 4 > M = 4 > > and execute printgraph tool with the following command line option: > > printgraph parms > > Best, > Synge > > > On 2014/09/29, at 11:03, Synge Todo <wistaria(a)comp-phys.org> wrote: > > > Dear Oleh, > > > > It seems that your lattice ?p_lat? is not defined in THREE dimensions, > but in TWO dimensions. > > Are you really simulating three-dimensional model? > > > > Best, > > Synge > > > > > > On 2014/09/29, at 5:09, Menchyshyn Oleh <oleh.menchyshyn(a)gmail.com> > wrote: > > > >> Dear ALPS community, > >> > >> I am trying to obtain the critical temperature for the 3D ferromagnetic > Heisenberg model S=1/2 on the cubic lattice with a unit cell which contains > 16 atoms. I have made the QMC "loop" simulations for the lattice with > dimensions L = 8, i.e. 8*8*8 unit cells, also for L=10, and L=12. > >> But there was just a little bend on the magnetisation curve as a sign > of the phase transition which should occur for the ferromagnetic model for > certain. I know I should use the Binder cumulant and the finite size > scaling to locate the phase transition point correctly. > >> I have enlarged my lattice to L=24, but simulation goes very-very > slowly. As I have limited resources to just tens of cores and I have a > feeling I would need to take L=32(48?) at least I want to ask: > >> > >> Based on your experience what order should be the THERMALIZATION and > SWEEPS parameters? > >> How can I estimate the computational complexity of my problem and the > time it would take? > >> Or maybe, I do anything wrong? > >> > >> A one more technical issue. The tutorial on the ALPS says that > correctness of a lattice definition can be checked with "printgraph" tool. > I used it with a couple definition files but all resulted in: > >> > >> Caught exception: parameter parse error at "<LATTICES> <LATTICEGRAPH > name="p" > >> > >> Just for a reference I put a definition of a lattice I know worked well > with simulation tools, but failed with "printgraph" > >> > >> <LATTICES> > >> <LATTICEGRAPH name="p_lat"> > >> <FINITELATTICE> > >> <LATTICE dimension="2"> > >> <BASIS> <VECTOR>1 0</VECTOR><VECTOR>0 1</VECTOR></BASIS> > >> </LATTICE> > >> <PARAMETER name="L"/> > >> <PARAMETER name="M"/> > >> <EXTENT dimension="1" size="L"/> > >> <EXTENT dimension="2" size="M"/> > >> <BOUNDARY type="periodic"/> > >> </FINITELATTICE> > >> <UNITCELL dimension="2" vertices="6"> > >> <VERTEX id="1"><COORDINATE> 0.6 0.2 </COORDINATE></VERTEX> > >> <VERTEX id="2"><COORDINATE> 0.6 0.6 </COORDINATE></VERTEX> > >> <VERTEX id="3"><COORDINATE> 0.2 0.6 </COORDINATE></VERTEX> > >> <VERTEX id="4"><COORDINATE> 0.2 0.2 </COORDINATE></VERTEX> > >> <VERTEX id="5"><COORDINATE> 0.8 0.4 </COORDINATE></VERTEX> > >> <VERTEX id="6"><COORDINATE> 0.4 0.8 </COORDINATE></VERTEX> > >> <EDGE type="2"><SOURCE vertex="1"/><TARGET vertex="2"/></EDGE> > >> <EDGE type="2"><SOURCE vertex="2"/><TARGET vertex="3"/></EDGE> > >> <EDGE type="2"><SOURCE vertex="3"/><TARGET vertex="4"/></EDGE> > >> <EDGE type="2"><SOURCE vertex="1"/><TARGET vertex="4"/></EDGE> > >> <EDGE type="3"><SOURCE vertex="1"/><TARGET vertex="5"/></EDGE> > >> <EDGE type="3"><SOURCE vertex="2"/><TARGET vertex="6"/></EDGE> > >> <EDGE type="1"><SOURCE vertex="2"/><TARGET vertex="5"/></EDGE> > >> <EDGE type="1"><SOURCE vertex="3"/><TARGET vertex="6"/></EDGE> > >> <EDGE type="3"><SOURCE vertex="3"/><TARGET vertex="5" offset="-1 > 0"/></EDGE> > >> <EDGE type="1"><SOURCE vertex="4"/><TARGET vertex="5" offset="-1 > 0"/></EDGE> > >> <EDGE type="3"><SOURCE vertex="4"/><TARGET vertex="6" offset="0 > -1"/></EDGE> > >> <EDGE type="1"><SOURCE vertex="1"/><TARGET vertex="6" offset="0 > -1"/></EDGE> > >> </UNITCELL> > >> </LATTICEGRAPH> > >> </LATTICES> > >> > >> > >> Best regards, > >> Oleh Menchyshyn >

2 1

complexity estimation for the 3D ferromagnetic Heisenberg model
by Menchyshyn Oleh 29 Sep '14

29 Sep '14

Dear ALPS community, I am trying to obtain the critical temperature for the 3D ferromagnetic Heisenberg model S=1/2 on the cubic lattice with a unit cell which contains 16 atoms. I have made the QMC "loop" simulations for the lattice with dimensions L = 8, i.e. 8*8*8 unit cells, also for L=10, and L=12. But there was just a little bend on the magnetisation curve as a sign of the phase transition which should occur for the ferromagnetic model for certain. I know I should use the Binder cumulant and the finite size scaling to locate the phase transition point correctly. I have enlarged my lattice to L=24, but simulation goes very-very slowly. As I have limited resources to just tens of cores and I have a feeling I would need to take L=32(48?) at least I want to ask: Based on your experience what order should be the THERMALIZATION and SWEEPS parameters? How can I estimate the computational complexity of my problem and the time it would take? Or maybe, I do anything wrong? A one more technical issue. The tutorial on the ALPS says that correctness of a lattice definition can be checked with "printgraph" tool. I used it with a couple definition files but all resulted in: Caught exception: parameter parse error at "<LATTICES> <LATTICEGRAPH name="p" Just for a reference I put a definition of a lattice I know worked well with simulation tools, but failed with "printgraph" <LATTICES> <LATTICEGRAPH name="p_lat"> <FINITELATTICE> <LATTICE dimension="2"> <BASIS> <VECTOR>1 0</VECTOR><VECTOR>0 1</VECTOR></BASIS> </LATTICE> <PARAMETER name="L"/> <PARAMETER name="M"/> <EXTENT dimension="1" size="L"/> <EXTENT dimension="2" size="M"/> <BOUNDARY type="periodic"/> </FINITELATTICE> <UNITCELL dimension="2" vertices="6"> <VERTEX id="1"><COORDINATE> 0.6 0.2 </COORDINATE></VERTEX> <VERTEX id="2"><COORDINATE> 0.6 0.6 </COORDINATE></VERTEX> <VERTEX id="3"><COORDINATE> 0.2 0.6 </COORDINATE></VERTEX> <VERTEX id="4"><COORDINATE> 0.2 0.2 </COORDINATE></VERTEX> <VERTEX id="5"><COORDINATE> 0.8 0.4 </COORDINATE></VERTEX> <VERTEX id="6"><COORDINATE> 0.4 0.8 </COORDINATE></VERTEX> <EDGE type="2"><SOURCE vertex="1"/><TARGET vertex="2"/></EDGE> <EDGE type="2"><SOURCE vertex="2"/><TARGET vertex="3"/></EDGE> <EDGE type="2"><SOURCE vertex="3"/><TARGET vertex="4"/></EDGE> <EDGE type="2"><SOURCE vertex="1"/><TARGET vertex="4"/></EDGE> <EDGE type="3"><SOURCE vertex="1"/><TARGET vertex="5"/></EDGE> <EDGE type="3"><SOURCE vertex="2"/><TARGET vertex="6"/></EDGE> <EDGE type="1"><SOURCE vertex="2"/><TARGET vertex="5"/></EDGE> <EDGE type="1"><SOURCE vertex="3"/><TARGET vertex="6"/></EDGE> <EDGE type="3"><SOURCE vertex="3"/><TARGET vertex="5" offset="-1 0"/></EDGE> <EDGE type="1"><SOURCE vertex="4"/><TARGET vertex="5" offset="-1 0"/></EDGE> <EDGE type="3"><SOURCE vertex="4"/><TARGET vertex="6" offset="0 -1"/></EDGE> <EDGE type="1"><SOURCE vertex="1"/><TARGET vertex="6" offset="0 -1"/></EDGE> </UNITCELL> </LATTICEGRAPH> </LATTICES> Best regards, Oleh Menchyshyn

2 2

antiferromagnetic phase of Hubbard model on Bethe lattice
by Duo Song 23 Sep '14

23 Sep '14

Dear all, I am trying the DMFT CT-HYB, Hirsch-Fye tutorial and I have a question on the antiferromagnetic property of the system. It is said that the system, a Hubbard model on the Bethe lattice with interaction [image: U=3D/\sqrt{2}] at half filling, enters an antiferromagnetic phase upon cooling. In other words, the neighboring sites have only one electron each with opposite spins at low temperature. But the sites of Bethe lattice are independent. How do you get coupling between sites to even know when they are spin alined or not? Best, Duo

2 1

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