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Physical explanation of the non-analyticities in the ising model in the vicinity of zero external field

Physics Asked by JKalle on February 7, 2021

In the Ising model when $T<T_C$ with $T_C$ being the Curie temperature, there is a finite jump of the mean magnetization per spin, $m$, as the external field crosses $0$ (goes from negative values to positive or vice versa). What is the physical explanation of this non-analyticity?

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