CLASSICAL HEISENBERG AND SPHERICAL MODEL ON NONCRYSTALLINE STRUCTURES

It is known that on regular lattices the spherical model is the large- n limit of classical Heisenberg O(n) models for all temperatures. Here we give a rigorous proof of the analogous result holding in the criti cal regime on disordered structures (representing e.g. amorphous mater ials, polymers, fractals). In particular, the large-n limit of critica l exponents for the Heisenberg model coincides with the critical expon ents of the spherical model. These can be exactly calculated and are s hown to depend only on the spectral dimension (d) over tilde of the st ructure. In addition, when (d) over tilde < 2, as it is the case for m any real structures, the critical exponents of all O(n) models coincid e with the corresponding ones for the spherical model, (C) 1998 Elsevi er Science B.V. All rights reserved.