All Questions
Tagged with simulations ising-model
47
questions
3
votes
1
answer
73
views
Ising Model magnetisation
I am simulating the 2D Ising Model and specifically looking at the time evolution of magnetisation $m$. Now, in the non-equilibrium state, magnetisation will grow as a power law with time $t$, if ...
1
vote
0
answers
16
views
Solving a system of equations involving Gaussian Integrals numerically [closed]
I wish to solve the following system of equations numerically in any software, I tried in Mathematica using the expectation functions, but I have a difficulty in understanding how to go about solving ...
1
vote
0
answers
93
views
Can the specific heat capacity in the Ising Model be negative?
Im working on a numerical method for the Ising model. I'm asked to calculate both the absolute magnetizetion and the specific heat capacity:
$$c = \frac{\beta^2}{N} \left( \langle H^2 \rangle - \...
1
vote
1
answer
121
views
Two-point-correlation in the 3D ising model
I am currently coding a 3D (Monte-Carlo) implementation of the Ising model, using the single spin-flip & Wolff algorithm.
So far, I was able to calculate all the interesting observables, like $M$ ...
- 43
2
votes
2
answers
128
views
Phase transition in Ising Model with local $\mathbb{Z}_2$ symmetry
I am studying the Ising model with a local $\mathbb{Z}_2$ gauge symmetry
\begin{equation}
\mathcal{H} = -\sum_{\text{plaquettes}} \sigma^z(\vec{x}, \vec{\mu})\sigma^z(\vec{x}+\vec{\mu}, \vec{\nu})\...
- 904
0
votes
0
answers
77
views
Question about Monte Carlo Simulation of 2D lattice Ising Model and Classical Heisenberg Model
I'm trying run and experiment with Monte Carlo Simulations of 2D lattice Ising Model and Classical Heisenberg Model.
I've made a brief research on both models and I saw that main differences of these ...
- 699
0
votes
1
answer
40
views
How to interpret weights of the Principal Component Analysis of the Ising model?
I'm trying to replicate the results obtained in this paper: https://arxiv.org/pdf/1606.00318.pdf
. On page 3 the autors mention that the fact that the weight of the first principal component is ...
- 185
1
vote
0
answers
51
views
Metropolis Monte-Carlo for magnetic system with $S > 1/2$ or arbitrary set of quantum systems
A well-known example of classical Monte-Carlo method application is Ising model with $S=1/2$.
As I understood, people there widely use it for any kind of magnetic materials following the same idea
$$
...
- 111
1
vote
0
answers
61
views
Difference between two Monte-Carlo methods in Ising model
I was working on a Monte-Carlo simulation of the Ising model. It seems that we have two different way to flip a single spin and I didn't quite understand the difference between them.
Say we have $N\...
- 21
0
votes
0
answers
40
views
How do I initialize the lattice/grid in a Potts Model?
I am studying the following:
Cellular Potts Model Tutorial
However, either this doesn't say anything about the grid/lattice initialization, or I failed to find any indication.
How do I initialize ...
user280949
0
votes
1
answer
604
views
Meaning of 'thermalization' in Markov Chain Monte Carlo simulations
In performing MCMC simulations, it is standard practice to 'equilibriate' or 'thermalize' the system and then discard the initial data before useful sampling is done.
My question is about the concept ...
- 3
2
votes
0
answers
211
views
Simulation time for Ising model of large systems
I have tried to run simulation for Ising model of large-size square lattices at the critical point. Mostly I use Python optimized with numba decorator for $L=256$ it takes approx 2.5 min with ...
0
votes
0
answers
181
views
What are the state-of-the-art methods for simulating a time-dependent transverse-field Ising model?
Consider a spin-1/2 Ising model with time-dependent transverse field:
$$ H = - \sum_{i<j} J_{i, j} \sigma^z_i \sigma^z_j - \Gamma(t) \sum_i \sigma^x_i$$
Given the initial state $|\psi(0)\rangle$ (...
- 43
4
votes
1
answer
646
views
Dimension of Hamiltonian & Diagonalizability
Often in condensed matter physics literature, one encounters a Hamiltonian that goes something like :
$$
H = \sum_{i=1}^{n} J_{i}\ S_{i}^{z} S_{i+1}^{z},
$$
where $J_{i}$ are the coupling constants, $...
- 648
1
vote
1
answer
277
views
Simulating the Ising Model, but with three states instead of two
Recall the homogeneous Ising energy of a configuration σ in the absence of a magnetic field is given by the Hamiltonian function
$$
H(\sigma) = -\sum_{\langle i~j\rangle} \sigma_i \sigma_j ,
$$
where ...
- 32
2
votes
0
answers
123
views
Spin glass observables in Monte Carlo simulations
I am currently simulating an Edwards-Anderson spin glass using standard Metropolis Monte Carlo techniques. The spins are placed on a 3D cubic lattice with periodic boundaries and take on Ising values (...
- 21
5
votes
0
answers
705
views
Decorrelation times for a 2D Ising Model over a range of temperatures
So, I'm trying to simulate the Ising Model on a 2D square lattice of spins. When exploring the auto correlation of the magnetisation:
Where the auto covariance: $$A(T) = \langle(M(t)\ - \langle M\...
- 508
3
votes
1
answer
128
views
Is there any point in doing Monte Carlo on classical 2D Ising spin systems? [closed]
The partition function of a classical Ising spin system with arbitrary bonds on any planar graph can be evaluated in polynomial time, through the FKT algorithm. And if I understand correctly, this ...
- 713
1
vote
1
answer
361
views
Generating Ising model steady state configurations
What is the most efficient way to simulate steady state configurations of the Ising model? I am just interested in having a large set of random steady state configurations of the 1D Ising model (with ...
- 712
1
vote
0
answers
163
views
Simulation of Quantum Ising Model
I curious to know if there is a way to do simulation of quantum ising model with transverse field.
The method I know is - do classical ising model simulation in d+1 dimension which essentially maps to ...
- 418
1
vote
0
answers
28
views
What methods can I use to find the minimum of a tranverse field Ising model?
I am trying to solve for the minimum of the hamiltonian of the form:
$$
H = \sum_{i,j} J_{ij}q(i)q(j) + g_i\sum_i x(i)
$$
where q(i) is the operator (I + z(i))/2 and z(i) and x(i) are pauli operators ...
- 11
0
votes
1
answer
384
views
Autocorrelation function problem in Monte Carlo simulation of 2D Ising model
Currently, I did a Monte Carlo simulation with the local update and Wolff cluster updated in 2D classical Ising model. I use the autocorrelation function to compare 2 different algorithm in critical ...
- 263
1
vote
3
answers
457
views
Averages of absolute values in Monte Carlo simulation of Ising Model
Consider the 2D Ising model in $0$ field, with Hamiltonian
$$ H=J\sum_{\langle i,j\rangle}\sigma_i\sigma_j$$
The magnetization per spin is defined as
$$M=\frac{1}{N}\sum_i \sigma_i $$
Where $N$ is ...
- 4,736
0
votes
2
answers
505
views
Fluctuating magnetization curve in ising model
I am working on Metropolis-Montecarlo algorithm for 2D Ising model in python partly based on this document. I ran the simulation for 100 times on a 25 x 25 lattice with external magnetic field B = 0. ...
- 494
1
vote
0
answers
745
views
Using MATLAB to simulate the Ising Model [closed]
I am using MATLAB to simulate a 1D Ising Chain. I am running into an issue where when trying to find heat capacity, my system has a tremendous amount of noise. I'll post my code and an image of the ...
- 171
1
vote
1
answer
100
views
Why are the autocorrelations larger for the energy at the critical temperature?
Considering a simulation with the Swendsen-Wang algorithm for the 3-D cubic lattice I wanted to have a look at the auto-correlations, and expecting it to be quite small considering Swendsen-Wang is a ...
- 1,772
0
votes
0
answers
336
views
How to calculate the autocorrelation function of magnetic susceptibility for the Ising model?
In the paper Wolff U. 1989. Physics Letters B. 228(3):379–82, the autocorrelation time of susceptibility, $\tau_\chi$ was calculated, but the way to do so was not clearly explained in the paper.
To ...
3
votes
1
answer
694
views
Magnetic susceptibility vs Monte Carlo step
I have some difficulties in understanding how to compute the magnetic susceptibility from a Monte Carlo simulation of the Ising model. I know that it is related to the magnetisation of the system by $\...
- 479
0
votes
2
answers
138
views
Evaluating the quality of Monte Carlo simulations for 3D Ising model
Suppose I have developed a new Monte Carlo method, and I plan to test this method on studying the magnetization of a 3D Ising model at some non-zero temperature $T$. The coupling is nearest neighbor, ...
- 713
2
votes
1
answer
249
views
Magnetic susceptibility error by binning Monte Carlo
I am studying the 2D Ising model using Monte Carlo simulations and I have learned the binning (or batching) method for the error statistical analysis. Following this discussion https://books.google.it/...
- 479