Low-temperature properties of an integrable spin-3/2 gas with weak external magnetic field

We study the low-temperature thermodynamic properties of an integrable spin-3/2 fermionic model. Many interesting kinds of fermionic pairs exist in the systems. By using the Wiener-Hopf method, we obtain the ground state and the equation of state at low temperatures. The ground-state energy without binding energy and Zeeman energy can be represented by the spinless free fermions with an effective mass and a quadratic correction of the weak external magnetic field. We also discuss the quantum criticality for the phase transition from vacuum state to the super Tonks-Girardeau-like phase near the strong coupling limit.