Context : M dwarfs are an important source of information when studying and probing the lower end of the Hertzsprung-Russell ( HR ) diagram , down to the hydrogen-burning limit .
Being the most numerous and oldest stars in the galaxy , they carry fundamental information on its chemical history .
The presence of molecules in their atmospheres , along with various condensed species , complicates our understanding of their physical properties and thus makes the determination of their fundamental stellar parameters more challenging and difficult .

Aims : The aim of this study is to perform a detailed spectroscopic analysis of the high-resolution H-band spectra of M dwarfs in order to determine their fundamental stellar parameters and to validate atmospheric models .
The present study will also help us to understand various processes , including dust formation and depletion of metals onto dust grains in M dwarf atmospheres .
The high spectral resolution also provides a unique opportunity to constrain other chemical and physical processes that occur in a cool atmosphere .

Methods : The high-resolution APOGEE spectra of M dwarfs , covering the entire H-band , provide a unique opportunity to measure their fundamental parameters .
We have performed a detailed spectral synthesis by comparing these high-resolution H-band spectra to that of the most recent BT-settl model and have obtained fundamental parameters such as effective temperature , surface gravity , and metallicity ( T _ { \mathrm { eff } } , \mathrm { log } g and [ Fe/H ] , respectively ) .

Results : We have determined T _ { \mathrm { eff } } , \mathrm { log } g and [ Fe/H ] for 45 M dwarfs using high-resolution H-band spectra .
The derived T _ { \mathrm { eff } } for the sample ranges from 3100 to 3900 K , values of \mathrm { log } g lie in the range 4.5 \leq \mathrm { log } g \leq 5.5 , and the resulting metallicities lie in the range -0.5 \leq [ Fe/H ] \leq +0.5 .
We have explored systematic differences between effective temperature and metallicity calibrations with other studies using the same sample of M dwarfs .
We have also shown that the stellar parameters determined using the BT-Settl model are more accurate and reliable compared to other comparative studies using alternative models .

Conclusions :