One common correlation function is the radial distribution function which is seen often in statistical mechanics and fluid mechanics. The correlation function can be calculated in exactly solvable models (one-dimensional Bose gas, spin chains, Hubbard model) by means of Quantum inverse scattering method and Bethe ansatz. In an isotropic XY model, time and temperature correlations were evaluated by Its, Korepin, Izergin & Slavnov. Higher-order correlation functions involve multiple reference points, and are defined through a generalization of the above correlation function by taking the expected value of the product of more than two random variables:  However, such higher order correlation functions are relatively difficult to interpret and measure. For example, in order to measure the higher-order analogues of pair distribution functions, coherent x-ray sources are needed. Both the theory of such analysis and the experimental measurement of the needed X-ray cross-correlation functions are areas of active research.