From a consideration of high temperature series expansions in ferromagnets and in spin glasses, we propose an extended scaling scheme involving a set of scaling formulas which expresses to leading order the temperature ($T$) and the system size ($L$) dependences of thermodynamic observables over a much wider range of $T$ than the corresponding one in the conventional scaling scheme. The extended scaling, illustrated by data on the canonical $2d$ ferromagnet and on the $3d$ bimodal Ising spin glass, leads to consistency in the estimates of critical parameters obtained from scaling analyses for different observables.

• Received 28 March 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.117202