Magnetic response in a one-dimensional attractive interacting system with extended Fermi surface

We study the effect of the magnetic field in a one-dimensional attractive interacting system with an extended Fermi surface. By the application of Abelian bosonization, we are able to show that elementary excitations in different regions of momentum space behave differently. There is evidence of a mixed phase. The system possess a paramagnetic gapless excitation in the presence of an infinitesimal magnetic field, though the system has a spin gap. We calculate the susceptibilities at different regions of momentum space. We also discuss the effect of finite temperature, and the interesting behavior of the spin component of the specific heat.