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

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Cited by in corpus (14)

• The critical behavior of three-dimensional Ising spin glass models
• The high-temperature expansions of the higher susceptibilities for the Ising model in general dimension d
• Beyond the Boltzmann factor for corrections to scaling in ferromagnetic materials and critical fluids
• Extended Scaling in High Dimensions
• Critical Behavior of the Three-Dimensional Ising model with Anisotropic Bond Randomness at the Ferromagnetic-Paramagnetic Transition Line
• An extended scaling analysis of the S=1/2 Ising ferromagnet on the simple cubic lattice
• Extended Scaling for the high dimension and square lattice Ising Ferromagnets
• The bimodal and Gaussian Ising Spin Glasses in dimension two revisited
• A comparative study of selected parallel tempering methods
• Extended scaling for ferromagnetic Ising models with zero-temperature transitions
• Critical scaling to infinite temperature
• Critical aspects of three-dimensional anisotropic spin-glass models
• Ising spin glasses in dimension two; universality and non-universality
• Large-order aspects of the delta-expansion in low-dimensional Ising models