Older models of Martian structure had relatively small, solid cores.
The low density of Mars suggested that Mars' core must contain considerably less iron (in comparison to the overall mass of the planet) than the other Terrestrial planets. Meanwhile, the lack of a global magnetic field suggested that the core, such as it is, was completely solid. Estimates of core size ranged from less than 30% of the size of the planet (if similar to iron meteorites) to a maximum of 60% of the size of the planet (if rich in sulfur and other lighter materials). (NASA, JPL, Voyager Team, Calvin Hamilton)
One recent (2001) model of Mars, based on its paleomagnetic field.
A partially liquid core produced global magnetic fields in the past, and fossil magnetism in rocks formed at that time, but has cooled to the point where although still liquid, it no longer has a large enough heat flow to be convective, and cannot support a significant planetary field. The estimated size of the core remains smallish (38 to 44% of the size of the planet), depending upon the amount of sulfur in the core. (David Stevenson, Cal Tech)
Another (2003) model of Mars, based on flexing caused by Solar tidal forces.
A wholly liquid core, about half the size of the planet, and of necessity containing substantial amounts of sulfur, also fails to produce any convection or magnetic field. (C. F. Yoder, A. S. Konopliv, D. N. Yuan, E. M. Standish, W. M. Folkner, NASA, JPL)