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 ...
- 4,696
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 ...
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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 ...
- 4,696
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 ...
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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 ...
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7
votes
Accepted
What is the fundamental difference between the Ising and Potts models?
Fundamentally, there is not much of a difference. A Potts model is a kind of generalized Ising model that includes more spin states. The Hamiltonians can be written with similar forms.
The Ising model ...
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7
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 ...
- 2,332
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
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 ...
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4
votes
Accepted
How can I identify phase transition from a plot of Ising model?
For a having a phase transitions, small changes in parameters like temperature or pressure causes a large-scale, qualitative change in the state of a system.
To characterize the state of the system, ...
- 22.3k
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 ...
4
votes
What is a "transient" state?
The excerpt that you gave us defines a steady state as one in which the state is not changing ($\frac{\textrm{d}\rho}{\textrm{d}t} = 0$) and a transient state in which the state is changing ($\frac{\...
- 33.6k
3
votes
Some questions about implementing Swendsen-Wang algorithm
If you follow the derivation of the Swendsen-Wang method as described on Wikipedia (1), you will see that it works whether the quantity $J_{nm}$ is same for all links or different for different kinds ...
- 2,673
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 is a "transient" state?
Transient state can be defined as a state in which $\frac{\text{d} \rho}{\text{dt}} \neq 0$, which, in an Ising Model MCMC (or any step-based) simulation, could be translated to $\frac{\text{d} M}{\...
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2
votes
Is there any useful application to estimating the expectation value for an Ising model without magnetic field?
"I know that one "hot question" about the Ising model is to be able to find its ground state. However this ground state in the absence of magnetic field is necessarily a tensor product (...
- 33.6k
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-...
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2
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 ...
- 21
1
vote
How do I initialize the lattice/grid in a Potts Model?
Suggestion by Erik Kjellgren:
"You can initialize it however you want, there is no correct way to initialize it. There might be better choices you can make depending on what you want to ...
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