2019/05/08 by Rong Wei, Wei, Rong Qiang
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1905.06183
openalex publication_date 2019/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There is no an accepted exact partition function (PF) for the three dimensional (3D) Ising model to our knowledge. Mainly based on the connection between the lattice Green function (LGF) for the simple cubic lattice and that for the honeycomb lattice, we infer an empirical partition function (EPF) for the simple cubic Ising model in the absence of an external magnetic field. This \rm EPF_\rm 3D=\frac12π3∫0π∫0π∫0πlog [2(2\cosh 32z + 3\sinh 22z + 2)(1)/(2) -2α\sinh 2z (cosω1 + cos ω2 + cosω3)] \rmdω1\rmdω2\rmdω3, α∈[√(2),√(3)] (where z=\fracεkT, ε the interaction energy, T the temperature, and k Boltzmann constant). When α=√(2), this EPF is consistent well numerically with the result from high temperature expansions by Guttmann and Enting (1993). The specific heat from this EPF approaches infinity non-logarithmically at the critical temperature Tc. \fracεkTc=\cosh-1[(1)/(4) (17-3√(17))]/2≈ 0.277212, which is greater than 0.221654 from the recent Monte Carlo study.