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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 ...
Principia Mathematica's user avatar
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 ...
rhombicosicodecahedron's user avatar
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 - \...
Gonzalo Chiva San Román's user avatar
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 $M$ ...
Dorek's user avatar
  • 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})\...
QFTheorist's user avatar
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 ...
M. Çağlar TUFAN's user avatar
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 ...
EigenAle's user avatar
  • 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 $$ ...
Kirill Vasin's user avatar
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\...
Judson Shen's user avatar
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 ...
user avatar
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 ...
Grifter's user avatar
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 ...
Alireza Valizadeh's user avatar
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 $|\psi(0)\rangle$ (...
haoyu's user avatar
  • 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, $...
self.grassmanian's user avatar
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 ...
garserdt216's user avatar
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 (...
Beaker's user avatar
  • 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\...
V.L. Proud's user avatar
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 ...
PeaBrane's user avatar
  • 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 ...
PianoEntropy's user avatar
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 ...
Kartik Chhajed's user avatar
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 ...
rosaniline's user avatar
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 ...
JensenPang's user avatar
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 ...
user2723984's user avatar
  • 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. ...
147875's user avatar
  • 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 ...
MurderOfCrows's user avatar
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 ...
B. Brekke's user avatar
  • 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 ...
Joshua_whi's user avatar
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 $\...
MariNala's user avatar
  • 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, ...
PeaBrane's user avatar
  • 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/...
MariNala's user avatar
  • 479
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 $h$...
Trebor's user avatar
  • 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} ...
Varun's user avatar
  • 65
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 ...
mehrdad's user avatar
  • 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 ?
v_g's user avatar
  • 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 ...
Drebin J.'s user avatar
  • 386
2 votes
1 answer
2k views

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 ...
stone-zeng's user avatar
0 votes
0 answers
127 views

What is order of the Wolff Cluster algorithm?

What is the order of the Wolff Cluster update algorithm for Ising Model 2D and 3D?
mehrdad's user avatar
  • 55
0 votes
1 answer
140 views

New to ising model, can't find answer to simple energy calculation

I'm trying to see why we get this energy config here As far as I understood, up/down or down/up contributes +, and same direction, ie up up or down down negative. So it should be all negative on the ...
user469216's user avatar
0 votes
0 answers
708 views

Critical slowing down in Monte-Carlo algorithm for classical 2D Ising Model

Why do local updates (i.e. local spin flips) near the phase transition in MC algorithm for classical 2D Ising model are said to be not "effective" and lead to incorrect critical indices? I understand ...
Whys's user avatar
  • 163
1 vote
1 answer
236 views

$\Delta E=0$ in $2$D Ising model - accept or not?

2D Ising model simulation using the Metropolis algorithm. There is one thing which I don't understand. The difference in energy $\Delta E$ between the initial state and the new state is: $\Delta E = ...
ad1v7's user avatar
  • 165
1 vote
1 answer
276 views

Ising simulation-dimensionless

My question is about dimensions in Ising model.When we want to simulate Ising we use dimensionless parameter as you know.We choose J to be 1 and also K equal 1 and when temperature is 2.26 then it's ...
jack's user avatar
  • 325
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 ...
Daniel Mahler's user avatar
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 ...
user46242's user avatar
  • 163
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 ...
Learning is a mess's user avatar
1 vote
0 answers
2k views

2D Ising model simulations: Wolff algorithm acceptance probability with an external magnetic field

I have implemented the Wolff algorithm to simulate a 2D ferromagnet. It works by building a cluster of like spins and flipping them all at once to move quickly through phase space. In the case of no ...
KBriggs's user avatar
  • 439
1 vote
2 answers
2k views

Acceptance probability 2D Ising Model

Disclaimer: I just found a possible solution - eventhough i don't really understand, whats wrong with my prior approach. Edit: I just tried to calculate it from scratch and found the following: $E ...
oerpli's user avatar
  • 255
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 ?
cosmicraga's user avatar