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Journal of Computational Physics

Direct calculation of the derivatives of the free energy for Ising models by a modified Kadanoff variational method

Chin‐Kun Hu, Peter H. Kleban

Published Oct 1, 1981• 4 citations
Publisher
DOI
10.1016/0021-9991(81)90124-8

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Direct calculation of the derivatives of the free energy for Ising models by a modified Kadanoff's variational method

Chin‐Kun Hu, Peter H. Kleban

We present a systematic procedure for the direct calculation of the free energy and its first and second derivatives for the Ising model in one to three dimensions with a wide class of symmetry properties. This renormalization group method is based on the modified Kadanoff's variational method (MKUM). This method is not only general but also very accurate numerically both near and far from the critical point. Further it includes correction to scaling effects not present in the standard linearized renormalization group treatment. This work describes the techniques and presents some illustrative results for the square latttice and body-centered cubic lattice with nearest neighbor interactions. A full treatment of our results will be given elsewhere. (Author)

Unknow•Feb 1, 1982•0 citations
The modified Kadanoff's variational method recently considered by us is applied to calculate the free energies and their derivatives for a three-dimensional Ising model with bcc structure and without external magnetic field. We find a critical point at kc=0.162134{k}_{c}=0.162134kc​=0.162134 and the associated critical indices $\ensuremath{\alpha}=0.12$, ${\ensuremath{\alpha}}^{\ensuremath{'}}=0.095$.
We present a systematic procedure for the direct calculation of the free energy and its first and second derivatives for the Ising model in one to three dimensions with a wide class of symmetry properties. This renormalization group method is based on the modified Kadanoff's variational method (MKUM). This method is not only general but also very accurate numerically both near and far from the critical point. Further it includes correction to scaling effects not present in the standard linearized renormalization group treatment. This work describes the techniques and presents some illustrative results for the square latttice and body-centered cubic lattice with nearest neighbor interactions. A full treatment of our results will be given elsewhere. (Author)