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

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

1996-09-24

arxiv.org/abs/cond-mat/9609235v1

Physica A 235 (1997) 573-576

Physics

Condensed Matter

6 pages, latex, 2 figures not included. To appear in Physica A

Scientific paper

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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