URL: http://www-spht.cea.fr/articles/T02/081 16th Nishinomiya-Yukawa Memorial Symposium, Nishinomiya, Japan, November 2001 http://fr.arxiv.org/abs/cond-mat/0204161In two-dimensional systems, it is possible transmute bosons into fermions by use of a Chern-Simons gauge field. Such a mapping is used to compute magnetization processes of two-dimensional magnets. The calculation of the magnetization curve then involves the structure of the Hofstadter problem for the lattice under consideration. Certain features of the Hofstadter butterfly are shown to imply the appearance of magnetization plateaus. While not always successfull, this approach leads to interesting results when applied to the 2D AF magnet \SrCu
