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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-CTR is soo slow". Actually it isn't. If you only re-key every GB or so of generated data you get a speed of about 12 CPU cycles needed for 16 bytes of ...


14

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 look into pseudo-random number generation in the last few years, for other algorithms. My question: Are there any other modern random number generators better ...


12

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 completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes ...


7

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 et al. Phys. Rev. B 59, 1008 (1999) [arXiv link]. Another excellent realizations include KCuF$_3$, which has stronger (but still low) interchain coupling, and ...


6

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 experiment and easy to extract from numerics (or with a well-established theoretical value). In practice, the choice of which quantity to use will depend on ...


5

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 of: single-body operators, squares of single-body operators, and single-body operators coupled to an Ising field with given dynamics. And you can also ...


5

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 Monte Carlo simulation and linear spin wave theory. SpinW also has a Python library available, although this is not yet a first-class citizen (you can't pip ...


5

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 generate a spin-interaction-only Hamiltonian. Then you can plug it all into a QMC that is designed just to handle spin (such as Stochastic Series Expansion). ...


4

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 consider different spin configurations and map the exchange 'J' into the total energy values from DFT. In the simplest form, if you have two magnetic atoms in your ...


4

Actual examples of 2D magnetic systems are MXenes and metal-organic adsorption monolayers.


3

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 if you want an exact solution, you need either some very clever analytical approach (only available for special cases), or you need to do exact diagonalization....


2

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 framework is suitable for this kind of problem. Please take a look at Nielsen et al. J. Chem. Phys. 139 (2013) 224706. The application of the Heisenberg ...


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