Mean-magnetization-length or magnetization ?

[JIANG]

I'm calculating Curie temperature, but I don't know which output flag to choose.  

What's the difference between magnetization, mean-magnetization-length, and mean-magnetization-length?

Best regard,

Jiang

[gabo...@gmail.com]

The Ni workshop example [1] uses the mean-magnetisation-length.  Column 2 (temperature) and column 7 (mean-magnetisation-length) seemed to recreate the Curie temperature plot for that example [2].

The magnetisation, mean-magnetisation-length, and mean-magnetisation-length are defined in the VAMPIRE manual [3]:

A unit vector [4] is m-hat = m/|m| with m as the vector and the length as |m|.  The magnetisation outputs the unit vector m-hat (or mx-hat, my-hat, and mz-hat components) and length |m|.

magnetisation-length outputs only the length |m|.

The magnetisation and magnetisation-length are at an instantaneous (single point) in time.

The mean-magnetisation-length is the length but it's time averaged <|m|>.

[1] https://github.com/richard-evans/vampire-workshop/blob/master/input-files/1_intro/1a_Ni/input

[2] https://groups.google.com/g/vampire-users/c/LS51ZlvZeyw/m/3gljoW54AwAJ

[3] https://vampire.york.ac.uk/resources/vampire-manual.pdf

[4] https://en.wikipedia.org/wiki/Unit_vector

Kind Regards,

Gavin

VAMPIRE user

[JIANG]

 I still have some questions about 

sim:time-steps-increment=1

sim:equilibration-time-steps=20000
sim:loop-time-steps=20000

What do time-steps-increment, equilibration-time-steps, and loop-time-steps mean? I know that in Metropolis algorism, one should do many times of "flips" for the spin configurations. Is this related to those "sim" parameters?

By the way, if I want to study the size effect on Curie temperature, is just changing dimensions:system-size ok? Or others like boundary conditions should also be modified? 

Best regard,

Jiang

[gabo...@gmail.com]

equilibration-time-steps - Believe this controls an initial time stage of the Curie simulation that is needed to converge the magnetization at a thermal equilibrium.

loop-time-steps - Looks like it controls the number of steps after the equilibration-time-steps for getting an average magnetization [1].  In other words, smooths the curve for the magnetization.

More time steps should be better but come at a cost of increased Monte Carlo simulation time [2].  Think this is applicable to loop-time-steps [3] and equilibration-time-steps.

Have a look at the normalized magnetization versus time steps figure at [4].  You might also check out the Curie temperature simulation using VAMPIRE YouTube video [5].

time-steps-increment - Seems to control the number of time steps between collecting samples of the magnetization.  Controls the amount of that data outputted to the screen or output file [6].

In the Metropolis algorithm, the spin configurations do look like they have some relation to time step parameters as the article at [7] has the sentence:

... at low temperatures a series of trial moves on the unit sphere will lead to most moves being rejected. Ideally a move acceptance rate of around 50% is desired, since very high and very low rates require significantly more Monte Carlo steps to reach a state representative of true thermal equilibrium.

Changing the dimensions:system-size seems like it would be okay if you just have magnetic region as a rectangular cubiod [8] such as a multilayer [9].  However, that would change if you have a different magnetic shape such as a sphere [10] or truncated octahedron [11].

Sure, if you have a finite shaped magnetic region, you should not need PBC (periodic boundary conditions).  However, if your magnetic shape is pseudo-infinite (e.g., nanotube, thin film, etc.), then PBC could be beneficial for your modeling of the magnetic material [12].

[1] https://groups.google.com/g/vampire-users/c/RAHCvweTmsA/m/iaUVB-1M5S8J

[2] http://albi3ro.github.io/M4/Monte-Carlo-Ferromagnet.html

[3] Page 48: https://pure.qub.ac.uk/en/studentTheses/ddf51d0f-1429-4f82-a703-54aad260d5c5

[4] https://vampire.york.ac.uk/tutorials/simulation/curie-temperature/

[5] https://www.youtube.com/watch?v=W5ivNgUklr8

[6] https://groups.google.com/g/vampire-users/c/anXElOPSSh8/m/Wj4CX0tBSQ8J

[7] https://doi.org/10.1088/0953-8984/26/10/103202

[8] https://en.wikipedia.org/wiki/Rectangular_cuboid

[9] https://vampire.york.ac.uk/tutorials/system-generation/multilayers/

[10] https://vampire.york.ac.uk/tutorials/system-generation/sphere/

[11] https://vampire.york.ac.uk/tutorials/system-generation/truncated-octahedron/

[12] https://vampire.york.ac.uk/tutorials/system-generation/periodic-boundaries/

Kind Regards,

Gavin

VAMPIRE user

[JIANG]

Thanks Gavin!