2D Ising model Monte-Carlo (Metropolis) method.

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Presentation transcript:

2D Ising model Monte-Carlo (Metropolis) method

2D Ising model Monte-Carlo (Metropolis) method

Some Ferromagnetic Elements Some Paramagnetic Elements • Iron • Uranium • Nickel • Platinum • Cobalt • Aluminum • Gadolinium • Sodium • Dysprosium • Oxygen

Magnetic dipole–dipole interaction

Energy Magnetization

T<<Tc T ~Tc T>> Tc Almost at the Close to the phase High temperature ground state transition (no correlation between spins) Single large cluster Broad distribution All clusters of like of ordered spins of clusters spins are small with small clusters of opposite spins

Monte-Carlo method

Onsanger exact result H=0, kB=1, J=1 for critical temperature T~Tc=2.269 T<<Tc T>>Tc

The mean average over all configurations= Yang exact result for H=0 forr magnetization Ergodic principle After thermalization The mean average over all configurations= The mean time average over 1 configuration

The thermalization depends on the size of the lattice and the number of steps

http://iopscience.iop.org/article/10.1088/1367-2630/18/2/023008 A new look on the two-dimensional Ising model: thermal artificial spins amorphous Co68Fe24Zr8 NxN lattice , N=10487