  We investigate the low temperature thermodynamics and correlation functions
of one-dimensional spin-1/2 fermions with strong repulsion in an external
magnetic field via the thermodynamic Bethe ansatz method. The exact
thermodynamics of the model in a weak magnetic field is derived with the help
of Wiener-Hopf techniques. It turns out that the low energy physics can be
described by spin-charge separated conformal field theories of an effective
Tomonaga-Luttinger liquid and an antiferromagnetic SU(2) Heisenberg spin chain.
However, these two types of conformally invariant low-lying excitations may
break down as excitations take place far away from the Fermi points. The long
distance asymptotics of the correlation functions and the critical exponents
for the model in the presence of a magnetic field at zero temperature are
derived in detail by solving dressed charge equations and by conformal mapping.
Furthermore, we calculate the conformal dimensions for particular cases of
correlation functions. The leading terms of these correlation functions are
given explicitly for a weak magnetic field $H\ll 1$ and for a magnetic field
close to the critical field $H\rightarrow H_{c}$. Our analytical results
provide insights into universal thermodynamics and criticality in
one-dimensional many-body physics.
