Fundamental M-dwarf parameters from high-resolution spectra using PHOENIX ACES models: I. Parameter accuracy and benchmark stars

M-dwarf stars are the most numerous stars in the Universe; they span a wide range in mass and are in the focus of ongoing and planned exoplanet surveys. To investigate and understand their physical nature, detailed spectral information and accurate stellar models are needed. We use a new synthetic atmosphere model generation and compare model spectra to observations. To test the model accuracy, we compared the models to four benchmark stars with atmospheric parameters for which independent information from interferometric radius measurements is available. We used $\chi^2$ -based methods to determine parameters from high-resolution spectroscopic observations. Our synthetic spectra are based on the new PHOENIX grid that uses the ACES description for the equation of state. This is a model generation expected to be especially suitable for the low-temperature atmospheres. We identified suitable spectral tracers of atmospheric parameters and determined the uncertainties in $T_{\rm eff}$, $\log{g}$, and [Fe/H] resulting from degeneracies between parameters and from shortcomings of the model atmospheres. The inherent uncertainties we find are {\sigma}$T_{\rm eff}$= 35 K, {\sigma}$\log{g}$ = 0.14, and {\sigma}[Fe/H] = 0.11. The new model spectra achieve a reliable match to our observed data; our results for $T_{\rm eff}$ and $\log{g}$ are consistent with literature values to within 1{\sigma}. However, metallicities reported from earlier photometric and spectroscopic calibrations in some cases disagree with our results by more than 3 {\sigma}. A possible explanation are systematic errors in earlier metallicity determinations that were based on insufficient descriptions of the cool atmospheres. At this point, however, we cannot definitely identify the reason for this discrepancy, but our analysis indicates that there is a large uncertainty in the accuracy of M-dwarf parameter estimates.