The thermodynamic geometry of the hadron resonance gas model with (without) excluded volume effects (EVE) of baryons is investigated. The case with imaginary $\mu$, where $\mu$ is the baryon chemical potential, is investigated as well as the one with real $\mu$. We calculate the scalar curvature $R$ and use the $R=0$ criterion to investigate the phase structure in the ${\mu }^2-T$ plane where $T$ is the temperature. The curve on which $R=0$ continues analytically from the imaginary $\mu$ region, where the lattice QCD is feasible, to the real $\mu$ one. In the presence of EVE, there are rich phase structures in the large real $\mu$ region as well as the Roberge-Weiss-like region where $\mu$ is imaginary and a singularity appears, while there is no phase structure in the large real $\mu$ region in the absence of EVE. The limiting temperature of the baryon gas is also obtained by using the baryon number fluctuation. The LQCD predicted critical point locates almost on the curve of the limiting temperature we determined. A simple empiric sufficient condition, $n_{\mathrm{B}}>1/(2v_{\mathrm{B}})$, is obtained for the quark deconfinement in the large real $\mu$ region, where $n_{\mathrm{B}}$ and $v_{\mathrm{B}}$ are the net baryon number density and the volume of a baryon, respectively.

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• Color confinement
• Nuclear matter
• Particle interactions
• QCD phase transitions
• Quantum chromodynamics
• Quark matter
• Quark-gluon plasma
• Thermal & statistical models