Abstract
We present an analysis of two problems in thermodynamics in terms of the Lambert W function, including the mean-field approximation of the Ising model, and Bose–Einstein condensation. Both problems are well known to exhibit the critical behavior of phase transition. Standard treatment of the problems involves numerical or graphical solutions. Utilizing justified simplifying approximations, we find a closed-form mean-field solution for the Ising model in terms of the special W function. With the same special function, we present an analysis of Bose–Einstein condensation, allowing approximate quantitative determination of the dependence of the chemical potential on temperature without full numerical computation. The analysis helps to facilitate understanding and to gain insight on these processes involving phase transitions in a straightforward manner.
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