Role of the sim:integrator in the Curie temperature program

[Jaime Garrido]

Hi Vampire users!

I just started using Vampire recently, so I am still new to both vampire itself and the theoretical background behind. I am mainly interested in using the Curie temperature program.

There is one line of the input file given in https://vampire.york.ac.uk/resources/tutorials/curie-temperature/input that I do not understand. The line is sim:integrator=monte-carlo. 

I do not get the role of the flag sim:integrator in the context of the Curie-temperature program.

What I understand is that the rotation of the spins is controlled by the flag montecarlo:algorithm. For example, montecarlo:algorithm=spin-flip flips the spins so that the simulation is Ising like.

But once enough monte-carlo steps (spin flips) have been done, the magnetization can be computed exactly (right?). It should be summing up all the contributions of the spins of the lattice. Hence, I do not understand what integral must be calculated so that an integrator must be chosen.

Maybe the word "integrator" is not related to any integral at all. But then, what is the role of this input option?

Thanks in advance 

Jaime

[gabo...@gmail.com]

The webpage at [1] mentions that sim:integrator=monte-carlo specifies an equilibrium properties calculation.

It looks like slide 24 in [2] has a comparison of Curie temperature calculations that used Monte Carlo (sim:integrator=monte-carlo) and LLG, where the results between the two look similar.  That slide also differentiates from Monte Carlo that the LLG is for a dynamics properties calculation.  The LLG for that slide probably means sim:integrator=llg-heun.

The post at [3] seems like it has some helpful advice between the Monte Carlo and LLG.

In the article on the VAMPIRE software at [4], section "4.1. Monte Carlo methods" of that article cites the Monte Carlo metropolis algorithm, which I'm thinking refers to the sim:integrator=monte-carlo.

A webpage that came up in a Google search on the Monte Carlo metropolis algorithm has a description on Monte Carlo integration that might be helpful.  The link for that should be [5].

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

[2] https://vampire.york.ac.uk/resources/workshop2017_day1.pdf

[3] https://groups.google.com/g/vampire-users/c/RAHCvweTmsA/m/ZbXv3GDw90AJ

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

[5] https://compphys.quantumtinkerer.tudelft.nl/proj2-monte-carlo/

Kind Regards,

Gavin

VAMPIRE user