visualization of the spin configuration
Energy
\(\displaystyle \frac{E}{N}\)
\(=\)
Magnetization
\(\displaystyle \frac{M}{N}\)
\(=\)
\(\displaystyle \frac{1}{N}\)
\(\displaystyle \sum_i \sigma_i\)
\(=\)
Heat capacity
\(\displaystyle \frac{C}{N k_{\mathrm{B}}}\)
\(=\)
\(\displaystyle \frac{1}{N}\)
\(\displaystyle \frac{\langle E^2 \rangle - \langle E \rangle^2}{(k_{\mathrm{B}} T)^2}\)
\(=\)
Susceptibility
\(\displaystyle \frac{\chi}{N}\)
\(=\)
\(\displaystyle \frac{1}{N}\)
\(\displaystyle \frac{\langle M^2 \rangle - \langle M \rangle^2}{k_{\mathrm{B}} T}\)
\(=\)

Ising Model Simulation

with the Metropolis Algorithm
Repository on GitHub
Simulation speed
Temperature
\(k_{\mathrm{B}} T =\)
Size
\(N =\)
\(\times\)
\(\displaystyle E = - \sum_{\langle i \, j \rangle} J_{i j} \sigma_i \sigma_j - h \sum_i \sigma_i\)
Allowed states
\(\sigma\)
Coupling constants
\(J\)
Horizontal
Vertical
Diagonal
Diagonal
Self
External field
\(h =\)