New Algorithm of the Finite Lattice Method for the High-temperature Expansion of the Ising Model in Three Dimensions

Abstract

We propose a new algorithm of the finite lattice method to generate the high-temperature series for the Ising model in three dimensions. It enables us to extend the series for the free energy of the simple cubic lattice from the previous series of 26th order to 46th order in the inverse temperature. The obtained series give the estimate of the critical exponent for the specific heat in high precision.

4 pages, 4 figures, submitted to Phys. Rev. Letters

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• Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity
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• Updated tests of scaling and universality for the spin-spin correlations in the 2D and 3D spin-S Ising models using high-temperature expansions
• Kallen-Lehman approach to 3D Ising model
• Minimal duality breaking in the Kallen-Lehman approach to 3D Ising model: a numerical test
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• Estimates of critical quantities from an expansion in mass: Ising model on the simple cubic lattice