# Visualizing the 2D Ising Model with Monte Carlo Algorithm

• C/C++
• maverick280857
In summary: Since the program hangs after the last iteration, I'm guessing that something is wrong with the data. I'll have to look into it more.
maverick280857
Hi,

So I'm trying to solve the 2D Ising Model using a simple Monte Carlo algorithm, for small square lattices, imposing periodic boundary conditions. Before I compute any thermodynamic quantities though, I want to study the energetics of the system with only nearest-neighbour interactions.

I want to visualize the system at every iteration of the Monte Carlo loop. The idea is to store the state of the lattice in a matrix, with each site storing the value +1 for spin up, and -1 for spin down.

A computer program I've written in C with a friend generates a data file with the state of the matrix. I then use a pipe to call gnuplot from within this program, to plot the file.

However, I notice that the plot window appears only after the pipe is closed -- presumably it is then that gnuplot is actually executed the first time, with all the arguments sent through the pipe. This means the plot window does not show up at a specific time of your choice, and in fact shows up at the end of the program.

Now, I want to visualize the matrix at every iteration, so for that, I need to call gnuplot (through the same pipe pointer) in every iteration, so that the existing plot is updated. How can this be done?

If I just naively include a plot command (through fprintf), then the plot shows up for the first time after some 20 or 30 iterations (depending on the size of the lattice).

you may need to flush the pipeline. If the C output is buffered, it will only be written when the buffer is full, or when the file/pipe is closed. You can manually trigger the flushing using fflush(file handle). Otherwise there may be a flag to open the pipe in an unbuffered mode.

M Quack said:
you may need to flush the pipeline. If the C output is buffered, it will only be written when the buffer is full, or when the file/pipe is closed. You can manually trigger the flushing using fflush(file handle). Otherwise there may be a flag to open the pipe in an unbuffered mode.

Thanks M Quack! Using fflush after every fprintf seems to have done the trick. However, I get the following error after the last iteration, and the program simply hangs (without exiting).

Code:
glibc detected *** ./ising: corrupted double-linked list: 0x000000000093e000 ***

No clue. Make sure Gnuplot exits normally (send exit command) before you kill the pipe?!? Otherwise throw in a hand full of print commands to see how far it goes and where it hangs.

Dear researcher,

Thank you for sharing your work on the 2D Ising Model with Monte Carlo Algorithm. Visualizing the system at every iteration is a great way to understand the dynamics of the system. It is understandable that you are facing some challenges in updating the plot in each iteration.

One way to solve this issue is to use the "refresh" command in gnuplot, which allows you to update a plot without closing the window. You can use a loop in your program to continuously update the plot using this command. Another option is to use a different plotting software that allows for live updating, such as Matplotlib or Plotly.

Additionally, I would suggest considering using a more efficient method for updating the plot, such as only plotting every few iterations or only when there is a significant change in the system. This can help reduce the computational time and resources needed for plotting.

I wish you success in your research and hope that this response has been helpful. Keep up the good work!

Best,

## 1. What is the 2D Ising Model?

The 2D Ising Model is a mathematical model used to study the behavior of magnetic materials. It consists of a grid of spins (magnetic moments) that can be either up or down, representing the direction of the magnetic field. The interactions between neighboring spins can cause the system to exhibit phase transitions, such as from a magnetized to a non-magnetized state.

## 2. How does the Monte Carlo algorithm work?

The Monte Carlo algorithm is a simulation method used to calculate the average behavior of a system. In the case of the 2D Ising Model, it works by randomly flipping spins in the grid and calculating the resulting energy of the system. This process is repeated many times, and the average energy is used to determine the behavior of the system at different temperatures.

## 3. What is the significance of visualizing the 2D Ising Model?

Visualizing the 2D Ising Model allows scientists to better understand the complex behavior of magnetic materials at different temperatures. It also provides a visual representation of the phase transitions that occur in the system, which can be helpful in predicting the behavior of real-world materials.

## 4. What are some limitations of using the 2D Ising Model?

The 2D Ising Model is a simplified representation of real-world materials and does not take into account factors such as external magnetic fields or the three-dimensional nature of materials. Additionally, the model assumes that all interactions between spins are equal, which may not be the case in some materials.

## 5. How is the 2D Ising Model used in other areas of science?

The 2D Ising Model has applications in various fields of science, such as statistical mechanics, materials science, and computer science. It has also been used to study other systems, such as the behavior of proteins in biological systems and the spread of diseases in populations.

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