Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-12-28
Physics
Condensed Matter
Statistical Mechanics
10 pages, 14 figures; v2: revised some sections, 1 ref added
Scientific paper
10.1103/PhysRevB.76.134421
A simple systematic rule, inspired by high-temperature series expansion (HTSE) results, is proposed for optimizing the expression for thermodynamic observables of ferromagnets exhibiting critical behavior at $\Tc$. This ``extended scaling'' scheme leads to a protocol for the choice of scaling variables, $\tau=(T-\Tc)/T$ or $(T^2 - \Tc^2)/T^2$ depending on the observable instead of $(T-\Tc)/\Tc$, and more importantly to temperature dependent non-critical prefactors for each observable. The rule corresponds to scaling of the leading of the reduced susceptibility above $\Tc$ as $\chi_{\rm c}^{*}(T)\sim \tau^{-\gamma}$ in agreement with standard practice with scaling variable $\tau$, and for the leading term of the second-moment correlation length as $\xi_{\rm c}^{*}(T)\sim T^{-1/2}\tau^{-\nu}$. For the specific heat in bipartite lattices the rule gives $C_{\rm c}^{*}(T) \sim T^{-2}[(T^2 -\Tc^2)/T^2]^{-\alpha}$. The latter two expressions are not standard. The scheme can allow for confluent and non-critical correction terms. A stringent test of the extended scaling is made through analyses of high precision numerical and HTSE data, or {\it real} data, on the three-dimensional canonical Ising, XY, and Heisenberg ferromagnets.
Campbell Andrew I.
Hukushima Koji
Takayama Hajime
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