All Questions
Tagged with ising-model simulations
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:
$$c = \frac{\beta^2}{N} \left( \langle H^2 \rangle - \...
1
vote
1
answer
121
views
Two-point-correlation in the 3D ising model
I am currently coding a 3D (Monte-Carlo) implementation of the Ising model, using the single spin-flip & Wolff algorithm.
So far, I was able to calculate all the interesting observables, like $M$ ...
2
votes
2
answers
128
views
Phase transition in Ising Model with local $\mathbb{Z}_2$ symmetry
I am studying the Ising model with a local $\mathbb{Z}_2$ gauge symmetry
\begin{equation}
\mathcal{H} = -\sum_{\text{plaquettes}} \sigma^z(\vec{x}, \vec{\mu})\sigma^z(\vec{x}+\vec{\mu}, \vec{\nu})\...
0
votes
0
answers
77
views
Question about Monte Carlo Simulation of 2D lattice Ising Model and Classical Heisenberg Model
I'm trying run and experiment with Monte Carlo Simulations of 2D lattice Ising Model and Classical Heisenberg Model.
I've made a brief research on both models and I saw that main differences of these ...
0
votes
1
answer
40
views
How to interpret weights of the Principal Component Analysis of the Ising model?
I'm trying to replicate the results obtained in this paper: https://arxiv.org/pdf/1606.00318.pdf
. On page 3 the autors mention that the fact that the weight of the first principal component is ...
1
vote
0
answers
51
views
Metropolis Monte-Carlo for magnetic system with $S > 1/2$ or arbitrary set of quantum systems
A well-known example of classical Monte-Carlo method application is Ising model with $S=1/2$.
As I understood, people there widely use it for any kind of magnetic materials following the same idea
$$
...
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\...
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 ...
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 ...
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 $|\psi(0)\rangle$ (...
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, $...
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 ...