# Mean-field theory in 1D Ising model

A mean-field theory approach to the Ising-model gives a critical temperature $k_B T_C = q J$, where $q$ is the number of nearest neighbours and $J$ is the interaction in the Ising Hamiltonian. Setting $q = 2$ for the 1D case gives $k_B T_C = 2 J$. Based on this argument there would be a phase transition in the 1D Ising model. This is obviously wrong.

Is mean-field-theory invalid for the 1D case? Am I missing something here?

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