Re: [ALPS-users] Questions about MC Simulation of XY Model

26 Oct 2020

      Dear Professor Todo,

Sorry to bother you again. I have seen the spinsim.h file, which is very hard for me to understand the codes without detailed comments. Yesterday, I added the following code into the do_measurements function of spinsim.h:

```
if (M::dim == 2) {
    typename parent::site_iterator si;
    si=this->sites().first;

    double m_x = 0.;
    double m_y = 0.;

    m_x = this->spinfactor_[*si]*spins_[*si].mag_h({1.,0.});
    m_y = this->spinfactor_[*si]*spins_[*si].mag_h({0.,1.});

    ++si;

    for (; si !=this->sites().second ; ++si)
    {
      m_x += this->spinfactor_[*si]*spins_[*si].mag_h({1.,0.});
      m_y += this->spinfactor_[*si]*spins_[*si].mag_h({0.,1.});
    }

    double mx=m_x/this->num_sites();
    double my=m_y/this->num_sites();

    this->measurements.template get<alps::RealObservable>("Magnetization along x-axis") << mx;
    this->measurements.template get<alps::RealObservable>("Magnetization along y-axis") << my;

  }
```

I am still confused about how you perform the iteration of sites, so I just repeated what you have done for m, m_h and mst. Then I recompiled the spinmc, and it did give me some results. I just want to ask if is it correct to use .mag_h({1.,0.}) and .mag_h({0.,1.}) to get M_x and M_y? Or is there a better way?

Thank you,
Wei

On Oct 13, 2020, at 21:38, Synge Todo <wistaria@phys.s.u-tokyo.ac.jp<mailto:wistaria@phys.s.u-tokyo.ac.jp>> wrote:

Dear Wei,

As for <M_x^2>, it should be given by "Magnetization^2" divided by 2, as < Magnetization^2> = <M_x^2> + <M_y^2> = <M_x^2> / 2 for the XY model. As far as I know, <N_x>=<\cos 2\theta> is not implemented in the current version of spinmc. You have to write the code somewhere in applications/mc/spins/spinsim.h by your self. But, it should be straightforward.

Best,
Synge

On Oct 12, 2020, at 11:20, Wei Wang <wei.wang@jhu.edu<mailto:wei.wang@jhu.edu>> wrote:

Hi Professor Todo,

Sorry to bother you again. But what if I want to measure <M_x^2>=<\cos^2\theta> or the nematic <N_x>=<\cos 2\theta> of XY model by ALPS? I have googled it but didn't find anything related. Could you kindly give me some suggestions? Or I need to modify the source code of ALPS to achieve it?

Looking forward to your reply!

Regards,
Wei

On Sep 30, 2020, at 10:29, Synge Todo <wistaria@phys.s.u-tokyo.ac.jp<mailto:wistaria@phys.s.u-tokyo.ac.jp>> wrote:

Dear Wei,

Indeed, <\cos\theta> is zero if there is no external magnetic field.
If there is a non-zero magnetic field, 'Magnetization along Field' is the quantity you are looking for.

Best,
Synge

On Sep 30, 2020, at 11:03, Wei Wang <wei.wang@jhu.edu<mailto:wei.wang@jhu.edu>> wrote:

Dear Prof. Todo,

Thank you for your reply! I have added these two lines into my code, and print the measurements out:

set(['Magnetization^2', 'Binder Cumulant', 'Specific Heat', '|Magnetization|', 'Magnetization^4', '|Staggered Magnetization|', 'Staggered Magnetization^2', 'E.Magnetization^4’,
'E.Magnetization^2', 'Energy Density', 'Susceptibility', 'beta * Energy / sqrt(N)', 'Magnetization along Field', 'Magnetization^4 slope', 'Connected Susceptibility', 'Magnetization^2
slope', 'Binder Cumulant U2', 'Cluster size', 'Bond-type Energy', 'Energy', 'Bond-type Energy Density', 'Energy^2', '(beta * Energy)^2 / N', 'Binder Cumulant slope'])

I don’t find an observable like the <\cos\theta>, or which of the measurements above can give me the directions of the magnetization. Please forgive me if this is a silly question, I am a 1st-year graduate student learning how to use ALPS. Thank you!

Regards,
Wei

On Sep 30, 2020, at 09:45, Synge Todo <wistaria@phys.s.u-tokyo.ac.jp<mailto:wistaria@phys.s.u-tokyo.ac.jp>> wrote:

Dear Wei,

You can obtain a list of measurements by

data = pyalps.loadMeasurements(pyalps.getResultFiles(prefix='data/parmXY'))
measurements = { item.props['observable'] for item in pyalps.flatten(data) }

Best,
Synge

On Sep 30, 2020, at 9:49, Wei Wang <wei.wang@jhu.edu<mailto:wei.wang@jhu.edu>> wrote:

Hi,

I am just new to ALPS, and I have a silly question about running MC simulations of XY model:

Following the tutorials, I use python to run the simulations and change the model from “Ising” to “XY”, like:

import pyalps

parms = [
 {
     'LATTICE': "square lattice",
     'T': 1,
     'J': 1,
     'THERMALIZATION': 10000,
     'SWEEPS': 400000,
     'UPDATE': "cluster",
     'MODEL': "XY",
     'L': 8
 }
]

input_file = pyalps.writeInputFiles('data/parmXY', parms)
pyalps.runApplication('spinmc', input_file, Tmin=5)
result_files = pyalps.getResultFiles(prefix='data/parmXY')

data = pyalps.loadMeasurements(result_files)

how can I get some observables like <\cos\theta>, where \theta is the direction of the spin at each site? If such a quantity is not provided directly by ALPS, is there a possible method to get these quantities I want. I just get lost when I see the source code of ALPS.

Thank you in advance!

Best,
Wei

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