All Questions
19
questions
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 ...
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
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
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
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
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
72
views
What is this secondary transition in the simulation of the Ising model?
Here, the horizontal axis is the strength of the ambient magnetic field. The Hamiltonian I used is $$H = -h\sum_i \sigma_i - J\sum_{\langle i \, j \rangle}\sigma_i\sigma_j.$$ The horizontal axis is $h$...
- 487
0
votes
1
answer
240
views
Weird results of Monte Carlo simulation
I'm simulating the 3D Ising Model using the Wolff update algorithm.
I am using the Mersenne Twister RNG.
When the lattice size is $L = 50$, the specific heat curve looks very weird!!
I want to ...
- 55
1
vote
1
answer
120
views
Why are simulations like Monte Carlo or Metropolis studied for Ising Models when 1d and 2d case have analytical solutions?
I know that absolute analytical solutions exist for the 1d and 2d case but need some intuition as to why these simulation algorithms are used and how do we benefit from them ?
- 21
1
vote
1
answer
652
views
Flipping more than one spin in Metropolis Monte Carlo algorithms
In lattice systems such as Ising model or spin glasses, the standard Monte Carlo simulation with Metropolis algorithm works by proposig a single spin flip and then accepting or rejecting the proposal ...
- 386