Partition function (mathematics): Difference between revisions

Revision as of 03:47, 19 September 2019

Revision as of 03:48, 19 September 2019

Line 7:

==Definition==

Given a set of [[random variablesvariable]]s <math>X_i</math> taking on values <math>x_i</math>, and some sort of [[Scalar potential|potential function]] or [[Hamiltonian function|Hamiltonian]] <math>H(x_1,x_2,\dots)</math>, the partition function is defined as

:<math>Z(\beta) = \sum_{x_i} \exp \left(-\beta H(x_1,x_2,\dots) \right)</math>

Line 47:

For a collection of observables <math>H_k</math>, one would write

:<math>Z(\beta) = \mboxoperatorname{tr}\left[\,\exp \left(-\sum_k\beta_k H_k\right)\right]</math>

As before, it is presumed that the argument of tr is [[trace class]].