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

Abstract

We report a quasi-exact power law behavior for Ising critical temperatures on hypercubes. It reads $J/k_B{T}_c=K_0[(1-1/d)(q-1){]}^a$ 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.

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

References in corpus (1)

• Universal Formulae for Percolation Thresholds

Cited by in corpus (3)

• Square lattice site percolation at increasing ranges of neighbor interactions
• Site percolation on lattices with low average coordination numbers
• Two stroke Pumping Technique for Many-Body Systems