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Jess Riedel (talk | contribs) →Definition: Fixed paragraph made nonsensical by accidental removal of sentence SEVEN YEARS AGO. wow. |
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*'''translational symmetry''' yields ''C''(''s'',''s''<nowiki>'</nowiki>) = ''C''(''s'' − ''s''<nowiki>'</nowiki>) where ''s'' and ''s''<nowiki>'</nowiki> are to be interpreted as vectors giving coordinates of the points
*'''rotational symmetry''' in addition to the above gives ''C''(''s'', ''s''<nowiki>'</nowiki>) = ''C''(|''s'' − ''s''<nowiki>'</nowiki>|) where |''x''| denotes the norm of the vector ''x'' (for actual rotations this is the Euclidean or 2-norm).
Higher order correlation functions are often defined. A typical correlation function of order ''n'' is
:<math>C_{i_1i_2\cdots i_n}(s_1,s_2,\cdots,s_n) = \langle X_{i_1}(s_1) X_{i_2}(s_2) \cdots X_{i_n}(s_n)\rangle.</math>
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