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20 votes

What are good random number generators for Monte Carlo calculations?

Depending on how many random numbers you need in a short amount of time, it might be worth to consider using a cryptographic PRNG. In particular AES-CTR. Now of course you might say that "but AES-...
SEJPM's user avatar
  • 301
14 votes

What are good random number generators for Monte Carlo calculations?

It's been years since I've done Monte Carlo calculations (though it was more recent than the 90's!), so hopefully the information given below is still reasonably up-to-date. I've also had reason to ...
Anyon's user avatar
  • 4,751
12 votes
Accepted

Is Heisenberg model or in its simplier form Ising model a good approximation to study magnetic systems?

Introduction Your question reminds me of a quote by Paul Dirac, The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus ...
Anyon's user avatar
  • 4,751
8 votes

Is it possible to calculate/estimate the value of the J parameter to be used in the Heisenberg/Ising Hamiltonians?

The equation in your question, be it Heisenberg or Ising exchange, can be calculated by Energy mapping analysis. This has to be the most popular paper that discusses this technique. Basically, you ...
Xivi76's user avatar
  • 2,402
8 votes
Accepted

What are examples of materials that closely correspond to the Heisenberg model?

1D A famous example of a nearly ideal spin-$1/2$ isotropic Heisenberg antiferromagnetic chain (1D) system is copper pyrazine dinitrate [Cu(C$_4$H$_4$N$_2$)(NO$_3$)$_2$], which was discussed in Hammar ...
Anyon's user avatar
  • 4,751
6 votes

What measured quantity can be associated to the value of the J parameter in the Heisenberg/Ising hamiltonians?

Here I'll assume that the material is already believed to be roughly described by a model of the Heisenberg or Ising form. In that case, you just want a quantity that is easy to measure in your ...
taciteloquence's user avatar
5 votes

Are there interesting applications of estimating the energy for generalizations of the Heisenberg model?

When you have more than two Pauli operators in a single term, you can model multipolar terms, as described in this paper: ... multipolar correlators of order $p=1$ (spin, dipolar), $p=2$ (quadrupolar)...
Nike Dattani - No Free Time's user avatar
5 votes

Are there any codes to study magnetic materials?

Another option is ALF (Algorithms for Lattice Fermions), an auxiliary-field quantum Monte Carlo package. According to its website: it can simulate any Hamiltonian that can be written in terms of sums ...
stafusa's user avatar
  • 816
5 votes

Are there any codes to study magnetic materials?

In addition to those listed, Spin-W is another option: SpinW is a MATLAB library that can plot and numerically simulate magnetic structures and excitations of given spin Hamiltonian using classical ...
Matt Horton's user avatar
  • 1,531
5 votes

Are there any codes to study magnetic materials?

If you already know the electron spatial wavefunctions, then it should be possible to calculate the spin exchange coefficients between electrons on neighboring atoms (by directly integrating them) and ...
taciteloquence's user avatar
4 votes
Accepted

Are there interesting applications of estimating the energy for generalizations of the Heisenberg model?

It is probably worth mentioning that, in the context of strongly correlated electron system / antiferromagnetism / superexchange, the spin-spin interactions arise from perturbation theory. In the ...
Anyon's user avatar
  • 4,751
4 votes

What are examples of materials that closely correspond to the Heisenberg model?

Actual examples of 2D magnetic systems are MXenes and metal-organic adsorption monolayers.
user36313's user avatar
  • 730
4 votes

How to choose the values of J and spin parameters in a heterogeneous spin system?

The problem of defining the parameters comes fundamentally from using the Ising model. The Ising model is extremely simplistic, and is the most basic model of a phase transition. Magnetic materials ...
Richard Evans's user avatar
3 votes

What's the most efficient way to obtain the ground state of spin models exactly?

No, the quantum version is not simpler There are many ways to find the ground state of an arbitrary quantum system. Quantum Monte Carlo (QMC), Density Matrix Renormalization Group (DMRG), et. al., but ...
taciteloquence's user avatar
3 votes

Is it possible to calculate/estimate the value of the J parameter to be used in the Heisenberg/Ising Hamiltonians?

I agree with Xivi76. One can use this method to determine J. However, a supercell should be used and the two atoms chosen for the four states should not interact with their periodic image. If the ...
Shashank's user avatar
2 votes

Is it possible to calculate/estimate the value of the J parameter to be used in the Heisenberg/Ising Hamiltonians?

For normal DFT use Noodleman’s broken symmetry approach. Noodleman This one may be relevant for magnetic systems: PRB2019 Edited: in the supporting information (p. 9) of JACS 2017, 139, 18448, Kieber-...
MSwart's user avatar
  • 1,084
2 votes

What are examples of materials that closely correspond to the Heisenberg model?

The Heisenberg formalism is often used to describe the interaction between molecules adsorbed on a surface (2D) using a cluster expansion. This has nothing to do with magnetism, but the mathematical ...
Franziska Heß's user avatar

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