Extended Scaling for Ferromagnets

Abstract

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, $τ=(T-\Tc)/T$ 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 ${\chi }_{\mathrm{c}}^{\ast }(T)\sim {\tau }^{-\gamma }$ in agreement with standard practice with scaling variable $\tau$, and for the leading term of the second-moment correlation length as ${\xi }_{\mathrm{c}}^{\ast }(T)\sim T^{-1/2}{\tau }^{-\nu }$. For the specific heat in bipartite lattices the rule gives $C_{\rm c}^{*}(T) \sim T^{-2}[(T^2 -\Tc^2)/T^2]^{-α}$. 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.

10 pages, 14 figures; v2: revised some sections, 1 ref added

References in corpus (3)

• The critical exponents of the superfluid transition in He4
• Universality in three-dimensional Ising spin glasses: A Monte Carlo study
• An Extended Scaling Scheme for Critically Divergent Quantities in Ferromagnets and Spin Glasses

Cited by in corpus (5)

• The critical behavior of three-dimensional Ising spin glass models
• Beyond the Boltzmann factor for corrections to scaling in ferromagnetic materials and critical fluids
• Extended Scaling in High Dimensions
• Extended Scaling for the high dimension and square lattice Ising Ferromagnets
• Extended scaling for ferromagnetic Ising models with zero-temperature transitions