Lecture 1 (The Monte Carlo principle) - Institute for Particle Physics ...

MC techniques Quadratures Monte Carlo Simulation Summary
Why Metropolis is correct: Detailed balance
Consider one spin flip, connecting micro-states 1 and 2.
Rate of transitions given by the transition probabilities W
( )
If E 1 > E 2 then W 1→2 = 1 and W 2→1 = exp
− E 1−E 2
k B T
In thermal equilibrium, both transitions equally often:
P 2 W 2→1 = P 1 W 1→2
This takes into account that the respective states are
occupied according to their Boltzmann factors.
(P i ∼ exp(−E i /k B T))
In principle, all systems in thermal equilibrium can be
studied with Metropolis - just need to write transition
probabilities in accordance with detailed balance, as above
=⇒ general simulation strategy in thermodynamics.
F. Krauss IPPP
Introduction to Event Generators