Cold atom systems in optical lattices have long been recognized as an ideal platform for bridging condense matter physics and quantum optics. Here, we investigate the one-dimensional (1D) fermionic superradiance in an optical lattice, and uncover tricritical phenomena and multistability in finite-temperature cases. As a starting point, we compare the 1D and 2D Fermi gases in zero-temperature limit. It turns out that the tricritical point originates from the higher-order Fermi surface nesting and the infrared divergence in 1D systems, which is absent in 2D cases. For dissipative cavities, we obtain the stable phase diagram and observe a hysteresis-type evolution under quench dynamics. When extending to finite-temperature cases, we derive analytical expressions for the secosecond- and fourfourth-order Landau coefficients, matching the numerical phase diagrams well, and reveal two different trcritical behaviors, named as quantum- and classic-type tricritical points, respectively. In addition, we construct the dependence between the susceptibility and the temperature, giving a nontrivial scaling law ${lim}_{\mathrm{\Delta }T\to 0}\mathrm{\Delta }{B}_c\sim \mathrm{\Delta }{T}^{\nu }$ with $\nu >1$. This work provides an approach to understanding tricritical phenomena, multistability, and scaling rate of self-organized cold atoms.

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• Fermi gases
• Optical lattices & traps
• Phase transitions
• Superradiance & subradiance