Introduction to Mathematical Physics/Statistical physics/Some numerical computation in statistical physics

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In statistical physics, mean quantities evaluation can be done using by Monte--Carlo methods. in this section, a simple example is presented.

Example:

Let us consider a Ising model. In this spin system, energy can be written:

The following Metropolis algorithm [ma:compu:Stauffer93], [ma:compu:Koonin90] is used \index{Metropolis} to simulate probabilities :

  1. select spin to consider.
  2. evaluate variation of energy associated to a possible split of spin .
  3. compare a random number between zero and one with probability .
  4. split spin number (that is do ) i=f and only if .
  5. use the obtained configuration to compute mean quantities.