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-...
- 301
17
votes
Accepted
Ising model: How can I spot the critical point?
My question is, when I run a simulation with $N$ particles and I track the Hamiltonian per particle $(H/N)$ and the magnetization per particle $\left(\sum _i s_i /N\right)$, with $K$ values going from ...
- 4,451
14
votes
Ising model: How can I spot the critical point?
As Anyon correctly pointed out, there is no phase transition at finite temperature in 1D.
In 2D there are a number of different ways to identify the phase transition (I'm assuming you're using Monte ...
- 6,469
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 ...
- 4,451
11
votes
Is there a list of models that do and do not have the QMC sign problem?
You can tell if a Hamiltonian is sign-free by looking at it in the form that it is handed to you. If the Hamiltonian is real and the off-diagonals are non-positive then it is Stoquastic (which is sign-...
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11
votes
Is there a list of models that do and do not have the QMC sign problem?
The general problem of determining whether a Hamiltonian can be transformed into "stoquastic" (i.e. sign-problem-free) form by local transformations is NP-hard:
https://arxiv.org/abs/1906.08800
...
- 211
10
votes
Accepted
Autocorrelation function problem in Monte Carlo simulation of 2D Ising model
First, some general remarks:
The measurements should be made after the system has equilibrated, i.e., a large number of the first iterations should be discarded before the analysis.
They should also ...
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8
votes
Ising model: How can I spot the critical point?
I think Anyon's and taciteloquence's answers are perfect. I just want to add an emphasis on the following fact that frequently leads to confusion for beginners.
The formal definition of the ...
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8
votes
Autocorrelation function problem in Monte Carlo simulation of 2D Ising model
@stafusa's answer is great, but there is a specific phenomenon you are encountering here called critical slowing down, which is especially bad for the single-spin-flip Metropolis Algorithm.
Near the ...
- 6,469
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 ...
- 4,451
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 ...
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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)...
- 30.8k
5
votes
Ising models with many-body interactions
As a (very) incomplete answer to this question, here is one paper discussing the Ising FM with a plaquette term. Here specifically chosen because there was not a good cluster algorithm for it (so they ...
- 6,469
4
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 ...
- 2,232
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.
- 430
4
votes
How to choose starting magnetization while doing spin polarised calculation in Quantum ESPRESSO?
Is this the wrong assumption I am using for initializing starting_magnetization? If yes, What should be the right fact for choosing the initialization value?
The initial magnetization is not so ...
- 14.6k
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 ...
- 4,451
3
votes
How to choose half-Brillouin-zone (HBZ) in Fukui & Hatsugai's numerical scheme for the Z2 invariant?
I think I figured this out. For most practical purposes, I think it is fine to just choose $-\pi\leq k_x\leq \pi$ and $0\leq k_y\leq \pi$ (half-BZ, with exact ranges depending on the model). I think ...
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 ...
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3
votes
What packages exist for building quantum Monte Carlo simulations of spin or Hubbard Hamiltonians?
NECI (N-electron configuration interaction solver)
This is a free and open-source software written mainly in FORTRAN but with components in C/C++ and Python. It has been shown on a FeMoco calculation ...
- 30.8k
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 ...
- 313
2
votes
What packages exist for building quantum Monte Carlo simulations of spin or Hubbard Hamiltonians?
ALF (Algorithms for Lattice Fermions)
This is an auxiliary-field quantum Monte Carlo package. It's free, open-source, actively maintained (current version: 2.0, with 2.1 on the works — news are posted ...
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1
vote
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 ...
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