Abstract
We developed a systematic non-perturbative method base on Dyson-Schwinger theory and the derivable theory for Ising model at broken phase. Based on these methods, we obtain critical temperature and spin spin correlation beyond mean field theory. The spectrum of Green function obtained from our methods become gapless at critical point, so the susceptibility become divergent at Tc. The critical temperature of Ising model obtained from this method is fairly good in comparison with other non-cluster methods. It is straightforward to extend this method to more complicate spin models for example with continue symmetry.
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Acknowledgements
We thank Prof. Baruch Rosenstein for valuable discussions. The work was supported by the National Natural Science Foundation of China (Grant Nos. 11674007, 91736208, and 11920101004). The work was also supported by High-performance Computing Platform of Peking University.
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This article can also be found at http://journal.hep.com.cn/fop/EN/10.1007/s11467-021-1081-x.
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Liu, F., Fan, Z., Sun, Z. et al. Field theoretical approach to spin models. Front. Phys. 16, 63504 (2021). https://doi.org/10.1007/s11467-021-1081-x
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DOI: https://doi.org/10.1007/s11467-021-1081-x