On Jul 26, 2011, at 10:42 AM, zhian asadzadeh wrote:
Dear Matthias and Synge
I understood why there is that discrepancy for small clusters,
it is true that we can write the thermal energy as :
E(T)=\sum_{k} E(k)(2*n(k,T)-1)
but this expression is true for thermodynamic limit, because we know the model has an even and odd parity sectors which they must be diagonalized separately, for T=0 the ground state is in even sector, so the sum over K points are for anti periodic boundary conditions, but for finite temperature we cant arrive to that expression, unless with this approximation that H(odd)=H(even) which is true in the thermodynamic limit, because the dispersion will be continuous and there is no much difference between odd and even space K points.
for small sizes I checked the looper and exact diagonalization are same but with large difference with exact, but for large lattices the looper converges to exact result which is thermodynamic result:
for L=200, h=0.3
looper:: -0.9238482(6.21e-05) with SWEEPS=4000000
exact:: -0.92385063
@Synge
I took it from Magnetization density, I think also Magnetization in z direction is not zero,
ok, thanks I will try that.
Thanks,
Zhian
On Mon, Jul 25, 2011 at 12:00 PM,
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Today's Topics:
1. Quantum Monte Carlo for Ising in transverse field
(zhian asadzadeh)
2. Re: Quantum Monte Carlo for Ising in transverse field
(Matthias Troyer)
3. Re: Quantum Monte Carlo for Ising in transverse field (Synge Todo)
4. Custom measurements (Alexander Herzog)
----------------------------------------------------------------------
Message: 1
Date: Sun, 24 Jul 2011 12:48:03 +0200
From: zhian asadzadeh <zhian.asadzadeh@gmail.com>
Subject: [ALPS-users] Quantum Monte Carlo for Ising in transverse
field
To: comp-phys-alps-users@lists.phys.ethz.ch
Message-ID:
<CAEw6G6sEs2aaE8oY5S+dFob35edARq12xKp9=4h4BUdrZZ1i7g@mail.gmail.com>
Content-Type: text/plain; charset="iso-8859-1"
Dear Matthias,
by \Sigma_{i,j}, I mean \sum_{i,j},
for the exact result, we know the model is integrable, so by fermionization
and finally diagonalizing the Hamiltonian we will end up to an Hamiltonian
with sum over independent modes,
H=\sum_{k} E(k) (2 a_{k}^{dagger} a_{k}-1)
for the T=0 ground state energy, I have compared with DMRG results which are
exactly same, so I am sure up to this point the form of E(k) and my
summation over k space is correct.
so finally for E(T) simply we have:
E(T)=\sum_{k} E(k)(2*n(k,T)-1) in which n(k,T)=1/(exp(E(k)/T)+1) ::with
Boltzmann constant=1
Regards,
Zhian.
On Sun, Jul 24, 2011 at 12:00 PM, <
comp-phys-alps-users-request@lists.phys.ethz.ch> wrote:
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> Today's Topics:
>
> 1. Quantum Monte Carlo for Ising in transverse field
> (zhian asadzadeh)
> 2. Re: Quantum Monte Carlo for Ising in transverse field
> (Matthias Troyer)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Sat, 23 Jul 2011 16:29:39 +0200
> From: zhian asadzadeh <zhian.asadzadeh@gmail.com>
> Subject: [ALPS-users] Quantum Monte Carlo for Ising in transverse
> field
> To: comp-phys-alps-users@lists.phys.ethz.ch
> Message-ID:
> <CAEw6G6sPavSO0RMreyy701xo+LN4M4LGrBzOLJkonEKs9S=Wkw@mail.gmail.com
> >
> Content-Type: text/plain; charset="iso-8859-1"
>
> Dear Matthias,
>
> my intention is doing finite T QMC for 2D ising in transverse field with
> the following Hamiltonian:
> H=-J \Sigma_{i,j} S_{i}^{z} S_{j}^{z}-h \Sigma_{i} S_{i}^{x}
> but for checking the accuracy of the numeric I did some checks for 1D
> case which we can have an exact results,
> probably I am expecting too much accuracy, for example:
>
> L=100, T=0.32859
> Exact:: E(T)=-105.29789708270407, Mx(T)=0.27030367598168420
> looper:: E(T)=-105.61795 (0.00554), M(T)=0.4093185 (0.000138) ( I
> think it is in z direction)
> with SWEEPS:6000000, THERMALIZATION=2000000
>
> I have checked also for other sizes and very large SWEEPS.
> I don't expect to get exact result but I need much more accuracy in the
> calculated energy.
>
> and also other question: that magnetization which looper calculates is
> in the z direction?
> can I also measure M_{x} just with declaring it in parm file?
>
> Thanks a lot,
> Zhian.
>
>
> On Sat, Jul 23, 2011 at 12:00 PM, <
> comp-phys-alps-users-request@lists.phys.ethz.ch> wrote:
>
> > Send Comp-phys-alps-users mailing list submissions to
> > comp-phys-alps-users@lists.phys.ethz.ch
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> >
> >
> > Today's Topics:
> >
> > 1. restarting Lanczos iteration (jessica.alfonsi@unipd.it)
> > 2. Quantum Monte Carlo for Ising in transvers field (zhian asadzadeh)
> > 3. Re: Quantum Monte Carlo for Ising in transvers field
> > (Matthias Troyer)
> > 4. Re: restarting Lanczos iteration (Matthias Troyer)
> >
> >
> > ----------------------------------------------------------------------
> >
> > Message: 1
> > Date: Fri, 22 Jul 2011 12:22:47 +0200
> > From: jessica.alfonsi@unipd.it
> > Subject: [ALPS-users] restarting Lanczos iteration
> > To: comp-phys-alps-users@lists.phys.ethz.ch
> > Message-ID:
> > <5b0ae17b0813c63a97720e0fbc6cc1c6.squirrel@webmail.unipd.it>
> > Content-Type: text/plain;charset=utf-8
> >
> > Hi all,
> > I'd like to modify the Lanczos *.cpp examples in IETL example folder to
> be
> > able to restart the iteration from any interruption point during the
> > Lanczos iteration. I suppose first one has to dump some information, for
> > instance the cofficients of T-matrix and the starting vector, however the
> > more difficult part would be the resuming of the iteration. Can somebody
> > give me some hints on how accomplishing this task? Thanks in advance...
> >
> > Best regards,
> >
> > Jessica Alfonsi
> >
> >
> >
> >
> >
> > ------------------------------
> >
> > Message: 2
> > Date: Fri, 22 Jul 2011 13:03:23 +0200
> > From: zhian asadzadeh <zhian.asadzadeh@gmail.com>
> > Subject: [ALPS-users] Quantum Monte Carlo for Ising in transvers field
> > To: comp-phys-alps-users@lists.phys.ethz.ch
> > Message-ID:
> > <
> CAEw6G6vLtP2G8kviZ97cxgZy9Dv1x_MqyUzFWs9ejnM8WvwnmA@mail.gmail.com
> > >
> > Content-Type: text/plain; charset="iso-8859-1"
> >
> > Dear All,
> >
> > I am trying to do QMC at finite temperature for calculating the
> > magnetization of *Ising model in transverse field*, but I realized just
> > looper code is working for this model, ( the others codes doesn't work
> with
> > off diagonal matrix elements) but the result are not so good.
> > I am interested to modify dirloop_sse for this model, is it possible?
> > I appreciate your help,
> > Thanks,
> > zhian.
> > -------------- next part --------------
> > An HTML attachment was scrubbed...
> > URL: <
> >
> https://lists.phys.ethz.ch/pipermail/comp-phys-alps-users/attachments/20110722/3a51e71a/attachment-0001.htm
> > >
> >
> > ------------------------------
> >
> > Message: 3
> > Date: Fri, 22 Jul 2011 09:09:43 -0600
> > From: Matthias Troyer <troyer@phys.ethz.ch>
> > Subject: Re: [ALPS-users] Quantum Monte Carlo for Ising in transvers
> > field
> > To: comp-phys-alps-users@lists.phys.ethz.ch
> > Message-ID: <A3A66CE8-DA3B-4160-8952-42868D25C5AC@phys.ethz.ch>
> > Content-Type: text/plain; charset="iso-8859-1"
> >
> > Dear Zhian,
> >
> > What is the problem with the looper code? It should be perfect for a
> > nonfrustrated Ising model in a transverse field. What is your model?
> >
> > Best regards
> >
> > Matthias
> >
> >
> >
> > On 22 Jul 2011, at 05:03, zhian asadzadeh wrote:
> >
> > > Dear All,
> > >
> > > I am trying to do QMC at finite temperature for calculating the
> > magnetization of Ising model in transverse field, but I realized just
> looper
> > code is working for this model, ( the others codes doesn't work with off
> > diagonal matrix elements) but the result are not so good.
> > > I am interested to modify dirloop_sse for this model, is it possible?
> > > I appreciate your help,
> > > Thanks,
> > > zhian.
> >
> > -------------- next part --------------
> > An HTML attachment was scrubbed...
> > URL: <
> >
> https://lists.phys.ethz.ch/pipermail/comp-phys-alps-users/attachments/20110722/fa041e0c/attachment-0001.htm
> > >
> >
> > ------------------------------
> >
> > Message: 4
> > Date: Fri, 22 Jul 2011 09:35:31 -0600
> > From: Matthias Troyer <troyer@phys.ethz.ch>
> > Subject: Re: [ALPS-users] restarting Lanczos iteration
> > To: jessica.alfonsi@unipd.it, comp-phys-alps-users@lists.phys.ethz.ch
> > Message-ID: <F50F2D14-EF41-4772-A2F8-8C0533C8A54F@phys.ethz.ch>
> > Content-Type: text/plain; charset=us-ascii
> >
> > Hi Jessica,
> >
> > Resuming iterations is already possible now. The Lanczos algorithm allows
> > you to continue iterating with a new iteration object. In your case I
> would
> > not iterate until convergence but only for a fixed number of steps.
> >
> > Indeed, all you have to store are the member variables of the Lanczos
> (and
> > underlying T-matrix) object, as well as the two last vectors of the
> > iteration (not the starting vector!). It is not hard to add that.
> >
> > Matthias
> >
> >
> >
> > On 22 Jul 2011, at 04:22, jessica.alfonsi@unipd.it wrote:
> >
> > > Hi all,
> > > I'd like to modify the Lanczos *.cpp examples in IETL example folder to
> > be
> > > able to restart the iteration from any interruption point during the
> > > Lanczos iteration. I suppose first one has to dump some information,
> for
> > > instance the cofficients of T-matrix and the starting vector, however
> the
> > > more difficult part would be the resuming of the iteration. Can
> somebody
> > > give me some hints on how accomplishing this task? Thanks in advance...
> > >
> > > Best regards,
> > >
> > > Jessica Alfonsi
> > >
> > >
> > >
> >
> >
> >
> > End of Comp-phys-alps-users Digest, Vol 64, Issue 6
> > ***************************************************
> >
> -------------- next part --------------
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>
> ------------------------------
>
> Message: 2
> Date: Sat, 23 Jul 2011 08:37:23 -0600
> From: Matthias Troyer <troyer@phys.ethz.ch>
> Subject: Re: [ALPS-users] Quantum Monte Carlo for Ising in transverse
> field
> To: comp-phys-alps-users@lists.phys.ethz.ch
> Message-ID: <2CC37437-71F7-436F-91E6-4AFBFE1DEFFA@phys.ethz.ch>
> Content-Type: text/plain; charset="iso-8859-1"
>
> Dear Zhian,
>
> The energy should actually be exact within error bars. How did you get the
> exact result that you compare to? and what was Sigma in that example?
>
> Matthias
>
>
>
> On Jul 23, 2011, at 8:29 AM, zhian asadzadeh wrote:
>
> > Dear Matthias,
> >
> > my intention is doing finite T QMC for 2D ising in transverse field
> with the following Hamiltonian:
> > H=-J \Sigma_{i,j} S_{i}^{z} S_{j}^{z}-h \Sigma_{i} S_{i}^{x}
> > but for checking the accuracy of the numeric I did some checks for 1D
> case which we can have an exact results,
> > probably I am expecting too much accuracy, for example:
> >
> > L=100, T=0.32859
> > Exact:: E(T)=-105.29789708270407, Mx(T)=0.27030367598168420
> > looper:: E(T)=-105.61795 (0.00554), M(T)=0.4093185 (0.000138) ( I
> think it is in z direction)
> > with SWEEPS:6000000, THERMALIZATION=2000000
> >
> > I have checked also for other sizes and very large SWEEPS.
> > I don't expect to get exact result but I need much more accuracy in
> the calculated energy.
> >
> > and also other question: that magnetization which looper calculates
> is in the z direction?
> > can I also measure M_{x} just with declaring it in parm file?
> >
> > Thanks a lot,
> > Zhian.
> >
> >
> > On Sat, Jul 23, 2011 at 12:00 PM, <
> comp-phys-alps-users-request@lists.phys.ethz.ch> wrote:
> > Send Comp-phys-alps-users mailing list submissions to
> > comp-phys-alps-users@lists.phys.ethz.ch
> >
> > To subscribe or unsubscribe via the World Wide Web, visit
> > https://lists.phys.ethz.ch/listinfo/comp-phys-alps-users
> > or, via email, send a message with subject or body 'help' to
> > comp-phys-alps-users-request@lists.phys.ethz.ch
> >
> > You can reach the person managing the list at
> > comp-phys-alps-users-owner@lists.phys.ethz.ch
> >
> > When replying, please edit your Subject line so it is more specific
> > than "Re: Contents of Comp-phys-alps-users digest..."
> >
> >
> > Today's Topics:
> >
> > 1. restarting Lanczos iteration (jessica.alfonsi@unipd.it)
> > 2. Quantum Monte Carlo for Ising in transvers field (zhian asadzadeh)
> > 3. Re: Quantum Monte Carlo for Ising in transvers field
> > (Matthias Troyer)
> > 4. Re: restarting Lanczos iteration (Matthias Troyer)
> >
> >
> > ----------------------------------------------------------------------
> >
> > Message: 1
> > Date: Fri, 22 Jul 2011 12:22:47 +0200
> > From: jessica.alfonsi@unipd.it
> > Subject: [ALPS-users] restarting Lanczos iteration
> > To: comp-phys-alps-users@lists.phys.ethz.ch
> > Message-ID:
> > <5b0ae17b0813c63a97720e0fbc6cc1c6.squirrel@webmail.unipd.it>
> > Content-Type: text/plain;charset=utf-8
> >
> > Hi all,
> > I'd like to modify the Lanczos *.cpp examples in IETL example folder to
> be
> > able to restart the iteration from any interruption point during the
> > Lanczos iteration. I suppose first one has to dump some information, for
> > instance the cofficients of T-matrix and the starting vector, however the
> > more difficult part would be the resuming of the iteration. Can somebody
> > give me some hints on how accomplishing this task? Thanks in advance...
> >
> > Best regards,
> >
> > Jessica Alfonsi
> >
> >
> >
> >
> >
> > ------------------------------
> >
> > Message: 2
> > Date: Fri, 22 Jul 2011 13:03:23 +0200
> > From: zhian asadzadeh <zhian.asadzadeh@gmail.com>
> > Subject: [ALPS-users] Quantum Monte Carlo for Ising in transvers field
> > To: comp-phys-alps-users@lists.phys.ethz.ch
> > Message-ID:
> > <
> CAEw6G6vLtP2G8kviZ97cxgZy9Dv1x_MqyUzFWs9ejnM8WvwnmA@mail.gmail.com>
> > Content-Type: text/plain; charset="iso-8859-1"
> >
> > Dear All,
> >
> > I am trying to do QMC at finite temperature for calculating the
> > magnetization of *Ising model in transverse field*, but I realized just
> > looper code is working for this model, ( the others codes doesn't work
> with
> > off diagonal matrix elements) but the result are not so good.
> > I am interested to modify dirloop_sse for this model, is it possible?
> > I appreciate your help,
> > Thanks,
> > zhian.
> > -------------- next part --------------
> > An HTML attachment was scrubbed...
> > URL: <
> https://lists.phys.ethz.ch/pipermail/comp-phys-alps-users/attachments/20110722/3a51e71a/attachment-0001.htm
> >
> >
> > ------------------------------
> >
> > Message: 3
> > Date: Fri, 22 Jul 2011 09:09:43 -0600
> > From: Matthias Troyer <troyer@phys.ethz.ch>
> > Subject: Re: [ALPS-users] Quantum Monte Carlo for Ising in transvers
> > field
> > To: comp-phys-alps-users@lists.phys.ethz.ch
> > Message-ID: <A3A66CE8-DA3B-4160-8952-42868D25C5AC@phys.ethz.ch>
> > Content-Type: text/plain; charset="iso-8859-1"
> >
> > Dear Zhian,
> >
> > What is the problem with the looper code? It should be perfect for a
> nonfrustrated Ising model in a transverse field. What is your model?
> >
> > Best regards
> >
> > Matthias
> >
> >
> >
> > On 22 Jul 2011, at 05:03, zhian asadzadeh wrote:
> >
> > > Dear All,
> > >
> > > I am trying to do QMC at finite temperature for calculating the
> magnetization of Ising model in transverse field, but I realized just looper
> code is working for this model, ( the others codes doesn't work with off
> diagonal matrix elements) but the result are not so good.
> > > I am interested to modify dirloop_sse for this model, is it possible?
> > > I appreciate your help,
> > > Thanks,
> > > zhian.
> >
> > -------------- next part --------------
> > An HTML attachment was scrubbed...
> > URL: <
> https://lists.phys.ethz.ch/pipermail/comp-phys-alps-users/attachments/20110722/fa041e0c/attachment-0001.htm
> >
> >
> > ------------------------------
> >
> > Message: 4
> > Date: Fri, 22 Jul 2011 09:35:31 -0600
> > From: Matthias Troyer <troyer@phys.ethz.ch>
> > Subject: Re: [ALPS-users] restarting Lanczos iteration
> > To: jessica.alfonsi@unipd.it, comp-phys-alps-users@lists.phys.ethz.ch
> > Message-ID: <F50F2D14-EF41-4772-A2F8-8C0533C8A54F@phys.ethz.ch>
> > Content-Type: text/plain; charset=us-ascii
> >
> > Hi Jessica,
> >
> > Resuming iterations is already possible now. The Lanczos algorithm allows
> you to continue iterating with a new iteration object. In your case I would
> not iterate until convergence but only for a fixed number of steps.
> >
> > Indeed, all you have to store are the member variables of the Lanczos
> (and underlying T-matrix) object, as well as the two last vectors of the
> iteration (not the starting vector!). It is not hard to add that.
> >
> > Matthias
> >
> >
> >
> > On 22 Jul 2011, at 04:22, jessica.alfonsi@unipd.it wrote:
> >
> > > Hi all,
> > > I'd like to modify the Lanczos *.cpp examples in IETL example folder to
> be
> > > able to restart the iteration from any interruption point during the
> > > Lanczos iteration. I suppose first one has to dump some information,
> for
> > > instance the cofficients of T-matrix and the starting vector, however
> the
> > > more difficult part would be the resuming of the iteration. Can
> somebody
> > > give me some hints on how accomplishing this task? Thanks in advance...
> > >
> > > Best regards,
> > >
> > > Jessica Alfonsi
> > >
> > >
> > >
> >
> >
> >
> > End of Comp-phys-alps-users Digest, Vol 64, Issue 6
> > ***************************************************
> >
>
> -------------- next part --------------
> An HTML attachment was scrubbed...
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>
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> ***************************************************
>
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------------------------------
Message: 2
Date: Sun, 24 Jul 2011 08:11:11 -0600
From: Matthias Troyer <troyer@phys.ethz.ch>
Subject: Re: [ALPS-users] Quantum Monte Carlo for Ising in transverse
field
To: comp-phys-alps-users@lists.phys.ethz.ch
Message-ID: <5BF47457-B95E-4616-9709-A81B92053BFB@phys.ethz.ch>
Content-Type: text/plain; charset=iso-8859-1
On Jul 24, 2011, at 4:48 AM, zhian asadzadeh wrote:
> Dear Matthias,
>
> by \Sigma_{i,j}, I mean \sum_{i,j},
>
> for the exact result, we know the model is integrable, so by fermionization and finally diagonalizing the Hamiltonian we will end up to an Hamiltonian with sum over independent modes,
> H=\sum_{k} E(k) (2 a_{k}^{dagger} a_{k}-1)
>
> for the T=0 ground state energy, I have compared with DMRG results which are exactly same, so I am sure up to this point the form of E(k) and my summation over k space is correct.
>
> so finally for E(T) simply we have:
> E(T)=\sum_{k} E(k)(2*n(k,T)-1) in which n(k,T)=1/(exp(E(k)/T)+1) ::with Boltzmann constant=1
Are you sure that you use the same units for temperature, etc. As the looper code is exact I wonder where the problem is. Can you please repeat this for a small system, e.g. 8 spins, where we can use fulldiag to compare. Also, which boundary conditions did you choose? DId you do the DMRG with periodic boundary conditions?
Matthias
------------------------------
Message: 3
Date: Mon, 25 Jul 2011 11:17:26 +0900
From: Synge Todo <wistaria@comp-phys.org>
Subject: Re: [ALPS-users] Quantum Monte Carlo for Ising in transverse
field
To: comp-phys-alps-users@lists.phys.ethz.ch
Message-ID: <93E46CFE-E817-45F7-9C6A-5FD7DDECCE1D@comp-phys.org>
Content-Type: text/plain; charset="us-ascii"
Dear Zhian,
On 2011/07/23, at 23:29, zhian asadzadeh wrote:
> L=100, T=0.32859
> Exact:: E(T)=-105.29789708270407, Mx(T)=0.27030367598168420
> looper:: E(T)=-105.61795 (0.00554), M(T)=0.4093185 (0.000138) ( I think it is in z direction)
> with SWEEPS:6000000, THERMALIZATION=2000000
The magnetization ("Magnetization" or "Magnetization Density") measured in the looper code is
in z direction, and it should be exactly zero in the present case due to the symmetry. From which
observable did you take the above figures?
> and also other question: that magnetization which looper calculates is in the z direction?
Yes.
> can I also measure M_{x} just with declaring it in parm file?
Please try the following patch to applications/qmc/looper/path_integral.C, which adds an observable
named "Number of Site Operators". Since the average number of site operators is related to the total
site-term energy (in this case Zeeman term by the transverse field) by
- Gamma * <Sum(S_i^x)> = - T * <Number of Site Operators> + C
with C = Gamma/2 in the present specific case, the transverse magnetization per site is given by
<S_i^x> = T * <Number of Site Operators> / N / Gamma - 1/2
where T is the temperature, N the number of sites.
Best,
Synge
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Message: 4
Date: Mon, 25 Jul 2011 09:36:44 +0200
From: Alexander Herzog <A.Herzog@fkf.mpg.de>
Subject: [ALPS-users] Custom measurements
To: comp-phys-alps-users@lists.phys.ethz.ch, Matthias Troyer
<troyer@phys.ethz.ch>
Message-ID: <20110725093644.171825ax1ccd2jnw@mail.fkf.mpg.de>
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Hello everyone,
I wanted to calculate the value $<S_j^z S_{j+r}^z> for a classical
Heisenberg-like model as a function of $r$.
I thought typing
MEASURE_CORRELATIONS[Sz]=Sz
in the parameter-file, the usual conversion (paramert2xml filename)
and running by spinmc --write filename.xml would be sufficient to get
the job done, but somehow the output-file does only contain the
default measurements.
Any help would be highly appreciated
All the best,
Alex
End of Comp-phys-alps-users Digest, Vol 64, Issue 8
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