Temporal and spatial simulation analysis of PM2. 5 concentration in autumn and winter in the Guangdong Hong Kong Macao Bay Area

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Journal of Guangzhou University(Natural Science Edition) ›› 2022, Vol. 21 ›› Issue (3) : 55-66.

Temporal and spatial simulation analysis of PM2. 5 concentration in autumn and winter in the Guangdong Hong Kong Macao Bay Area

  • ZHANG Xiuzhi, CHEN Yuan
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Abstract

In this paper, the modified spin wave theory is applied to the Heisenberg ferromagnetic chain with the ferromagnetic long range interaction J0 / rp and antiferromagnetic nearest neighbor interaction J. The spin wave thermodynamics of the system are obtained within the self consistent method by constraining the total magnetization to be zero. It is shown that the ferromagnetic long range and antiferromagnetic nearest neighbor inter actions have great influence on the low temperature properties of the system. At low temperatures, it is found that the specific heat C exhibits the temperature dependent peak behavior which is induced by p and J, along with the specific heat coefficient C / T1 / ( p - 1) ; while the susceptibility coefficient  T2 shows the low temperature behavior with a minimum induced by p and J. For J = 0 and in the large p limit, our results agree well with the exact Bethe ansatz results and the quantum Monte Carlo data.

Key words

modified spin wave theory; Heisenberg ferromagnetic chain; long range interaction; nearest neighbor interaction

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Temporal and spatial simulation analysis of PM2. 5 concentration in autumn and winter in the Guangdong Hong Kong Macao Bay Area. Journal of Guangzhou University(Natural Science Edition). 2022, 21(3): 55-66
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