: How to calculate magnetization in SSE method?

[tomkeus]

Plz Help: How to calculate magnetization in SSE method??

I need help from someone experienced with Stochastic Series Expansion algorithm.

I'm working on SSE algorithm for lattice of isotropic Heisenberg spins and it works fine, well, mostly. I have nice values for energy and heat capacity, but i have problem with magnetization.

Since magnetization is diagonal in basis used in SSE method I have simply summed up spins for every configuration generated by algorithm but this gives very, very wrong results. Obviously something different must be done.

Can anyone help, please? I really need it.

 

[eljose79]

Calculating the magnetization using the Stochastic Series Expansion (SSE) method requires a few additional steps compared to calculating energy and heat capacity. Firstly, it is important to note that in the SSE method, the magnetization is defined as the sum of all the spin components in the lattice, rather than just the diagonal components. This is because the SSE algorithm generates configurations in the full spin space, not just the diagonal basis.

To calculate the magnetization, you will need to sum up the spin components for each configuration generated by the algorithm, as you have done. However, in order to account for the full spin space, you will also need to multiply this sum by a factor of 2^(N), where N is the number of spins in your lattice. This factor accounts for the different possible spin orientations in the full spin space.

Additionally, it is important to ensure that your algorithm is generating configurations with the correct weights. The weight of each configuration should be proportional to the Boltzmann factor exp(-E/kT), where E is the energy of the configuration, k is the Boltzmann constant, and T is the temperature. If your algorithm is not generating configurations with the correct weights, this could also lead to incorrect magnetization results.

I hope this helps with your calculation of magnetization using the SSE method. If you have any further questions or concerns, please don't hesitate to ask for clarification. Best of luck with your research!

 

[charng]

Calculating magnetization in the SSE method involves using the Boltzmann distribution to determine the probability of each spin configuration, and then taking the weighted average of the magnetization for each configuration. This can be done using the Metropolis algorithm, where each Monte Carlo step involves flipping a random spin and calculating the change in energy. The probability of accepting this spin flip is then determined by the Boltzmann distribution. This process is repeated for a large number of Monte Carlo steps, and the average magnetization is calculated from the final spin configuration.

Alternatively, the magnetization can also be calculated by taking the expectation value of the magnetization operator in the SSE basis. This involves summing over all possible spin configurations and weighting each configuration by its probability as determined by the Boltzmann distribution. This method can be more accurate, but also more computationally intensive.

I recommend consulting with a colleague or mentor who is experienced with the SSE method for further assistance and guidance. Additionally, there are many resources available online and in scientific literature that provide detailed explanations and examples of calculating magnetization in the SSE method. Good luck with your research.