All Questions
Tagged with simulations ising-model
47
questions
9
votes
2
answers
5k
views
Numerical Ising Model - Wolff algorithm and correlations
I'm doing some numerical Monte Carlo analysis on the 2 dimensional Ising model at the critical point. I was using the Metropolis 'single flip' evolution at first with success, though it suffers from ...
7
votes
1
answer
2k
views
Critical temperature and lattice size with the Wolff algorithm for 2d Ising model
When I run my implementation of the Wolff algorithm on the square Ising model at the theoretical critical temperature I get subcritical behaviour. The lattice primarily just oscillates between mostly ...
- 3,500
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: $$A(T) = \langle(M(t)\ - \langle M\...
- 508
4
votes
1
answer
646
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Dimension of Hamiltonian & Diagonalizability
Often in condensed matter physics literature, one encounters a Hamiltonian that goes something like :
$$
H = \sum_{i=1}^{n} J_{i}\ S_{i}^{z} S_{i+1}^{z},
$$
where $J_{i}$ are the coupling constants, $...
- 648
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
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
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 ...
2
votes
1
answer
2k
views
I'm getting weird autocorrelations when simulating an Ising model below the critical temperature
So I'm simulating an Ising model using Monte Carlo and the Metropolis algorithm. After letting it reach equilibrium, I try to calculate the autocorrelation of the magnetization. As long as the system ...
- 163
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
2
votes
1
answer
748
views
Local minima in Ising model in a Monte Carlo simulation
Is there any way to check whether in a Monte Carlo simulation using Ising model is stuck in any (false) local minima of energy or not, particularly in 3D system ?
- 550
2
votes
1
answer
2k
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Monte Carlo steps in Ising model Metropolis algorithm
In K.Binder's book Monte Carlo Simmulation in Statistical Physics 4th ed., one Monte Carlo step is defined as "one sweep through the lattice". However, in many other books and papers, the Monte Carlo ...
- 369
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.$$ The horizontal axis is $h$...
- 487
2
votes
1
answer
920
views
Periodic autocorrelation function for Ising model?
I am trying to calculate the autocorrelation time for a 2-D Ising model Monte Carlo simulation. As the autocorrelation function, I am using $$\chi (t) = \frac{1}{t_{max}-t} \sum_{t' = 0}^{t_{max}-t-1} ...
- 65
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 ...
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