The SPHINX M-dwarf Spectral Grid. I. Benchmarking New Model Atmospheres to Derive Fundamental M-Dwarf Properties

About 70-80% of stars in our solar and galactic neighborhood are M dwarfs. They span a range of low masses and temperatures relative to solar-type stars, facilitating molecule formation throughout their atmospheres. Standard stellar atmosphere models primarily designed for FGK stars face challenges when characterizing broadband molecular features in spectra of cool stars. Here, we introduce SPHINX--a new 1-D self-consistent radiative-convective thermochemical equilibrium chemistry model grid of atmospheres and spectra for M dwarfs in low-resolution (R~250). We incorporate the latest pre-computed absorption cross-sections with pressure-broadening for key molecules dominant in late-K, early/main-sequence-M stars. We then validate our grid models by acquiring fundamental properties (Teff, log(g), [M/H], radius, and C/O) for 10 benchmark M+G binary stars with known host metallicities and 10 M dwarfs with interferometrically measured angular diameters. Incorporating a Gaussian-process inference tool Starfish, we account for correlated and systematic noise in low-resolution (spectral stitching of SpeX, SNIFS, and STIS) observations and derive robust estimates of fundamental M dwarf atmospheric parameters. Additionally, we assess the influence of photospheric heterogeneity on acquired [M/H] and find that it could explain some deviations from observations. We also probe whether the model-assumed convective mixing-length parameter influences inferred radii, effective temperature, and [M/H] and again find that may explain discrepancies between interferometry observations and model-derived stellar parameters for cooler M dwarfs. Mainly, we show the unique strength in leveraging broadband molecular absorption features occurring in low-resolution M dwarf spectra and demonstrate the ability to improve constraints on fundamental properties of exoplanet hosts and late brown dwarf companions.