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A Quasi-exact Formula for Ising critical temperatures on Hypercubic Lattices

Serge Galam·Alain Mauger
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Abstract

We report a quasi-exact power law behavior for Ising critical temperatures on hypercubes. It reads $J/k_BT_c=K_0[(1-1/d)(q-1)]^a$ where $K_0=0.6260356$, $a=0.8633747$, $d$ is the space dimension, $q$ the coordination number ($q=2d$), $J$ the coupling constant, $k_B$ the Boltzman constant and $T_c$ the critical temperature. Absolute errors from available exact estimates ($d=2$ up to $d=7$) are always less than $0.0005$. Extension to other lattices is discussed.

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Serge Galam, Alain Mauger. 1996-09-24. A Quasi-exact Formula for Ising critical temperatures on Hypercubic Lattices. https://doi.org/10.1016/s0378-4371(96)00353-6

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