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The Mg I 12.32 and 12.22 $\mu$m lines are a pair of emission lines thatpresent a great advantage for accurate solar magnetic field measurement. Theypotentially contribute to the diagnosis of solar atmospheric parameters throughtheir high magnetic sensitivity. The goal of this study is to understand theradiation transfer process of these lines in detail and explore the ability ofmagnetic field diagnosis in the infrared. We calculated the Stokes profiles andresponse functions of the two Mg I 12 $\mu$m lines based on one-dimensionalsolar atmospheric models using the Rybicki-Hummer (RH) radiative transfer code.The integration of these profiles with respect to the wavelength was used togenerate calibration curves related to the longitudinal and transverse fields.The traditional single-wavelength calibration curve based on the weak-fieldapproximation was also tested to determine if it is suitable for the infrared.The 12.32 $\mu$m line is more suitable for a magnetic field diagnosis becauseits relative emission intensity and polarization signal are stronger than thatof the 12.22 $\mu$m line. The result from the response functions illustratesthat the derived magnetic field and velocity with 12.32 $\mu$m line mainlyoriginate from the height of 450 km, while that for the temperature is about490 km. The calibration curves obtained by the wavelength-integrated methodshow a nonlinear distribution. For the Mg I 12.32 $\mu$m line, the longitudinal(transverse) field can be effectively inferred from Stokes V/I (Q/I and U/I) inthe linear range below $\sim 600$ G ($\sim 3000$ G) in quiet regions and below$\sim 400$ G ($\sim 1200$ G) in penumbrae. Within the given linear range, themethod is a supplement to the magnetic field calibration when the Zeemancomponents are incompletely split.

Infrared diagnostics of the solar magnetic field with Mg I 12 $\mu$m lines: forward-model results