Simulating Glauber dynamics for the Ising model

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Why is it that many materials exhibit “spontaneous magnetization”? • At low temperatures, they are magnetic. • At high temperatures, they are not.
Electron “spins” and magnetization • W. Lenz (1920) proposed a model of ferromagnetism. That each electron possesses a “spin”. Parallel spins attract. Antiparallel spins repel. At sufficiently low temperatures, the spins should align. • Ernst Ising (1924), in his doctoral thesis advised by Lenz, formalized these ideas and examined a 1-D chain of such spins. si ∈ {−1, +1} Ei ∝ −sisj the “exchange energy”
Page 1: Simulating Glauber dynamics for the
Page 5 and 6: Total energy, the “Hamiltonian”
Page 7 and 8: Phase transition in M as function o
Page 9 and 10: Equilibrium • In equilibrium, Bol
Page 11 and 12: Detailed balance P (Si)P (Si → Sj
Page 13 and 14: Implementing the Glauber dynamics
Page 15 and 16: Issues • Critical slowing down (c
Page 17 and 18: Greedy coupled dynamics • Pick a
Page 19 and 20: Dynamics • Generate a random numb
Page 21: Online Resources Ising model simula

Simulating Glauber dynamics for the Ising model

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