Partition function (mathematics): Difference between revisions

Revision as of 10:10, 18 June 2013

Revision as of 11:00, 18 June 2013

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There exists at least one configuration <math>(x_1,x_2,\dots)</math> for which the probability is maximized; this configuration is conventionally called the [[ground state]]. If the configuration is unique, the ground state is said to be '''non-degenerate''', and the system is said to be [[ergodic]]; otherwise the ground state is '''degenerate'''. The ground state may or may not commute with the generators of the symmetry; if commutes, it is said to be an [[invariant measure]]. When it does not commute, the symmetry is said to be [[spontaneously broken]].

Conditions under which a ground state exists and is unique are given by the [[Karush–Kuhn–Tucker conditions]]; these conditions are commonly used to justify the use of the Gibbs measure in maximum-entropy problems.{{Citation needed|date=June 2013}}

==Normalization==