Abstract
The influence of the blackbody radiation field on the $g$ factor of light hydrogenlike ions is considered within the framework of quantum electrodynamics at finite temperature for bound states. One-loop thermal corrections are examined for a wide range of temperatures. The numerical results for $1s, 2s, 2{p}_{1/2}$, and $2{p}_{3/2}$ states are presented. It is shown that for excited states, finite temperature corrections to the bound-electron $g$ factor are close to the level of current experimental uncertainty even at room temperatures and can be discerned within the measurements anticipated in the near future.
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