  We explore how the spiral spin(SP) state, a spin singlet known to accompany
fully-polarized ferromagnetic (F) states in the Hubbard model, is related with
the F state in the thermodynamic limit using the density matrix renormalization
group and exact diagonalization. We first obtain an indication that when the F
state is the ground state the SP state is also eligible as the ground state in
that limit. We then follow the general argument by Koma and Tasaki [J. Stat.
Phys. {\bf 76}, 745 (1994)] to find that: (i) The SP state possesses a kind of
order parameter. (ii) Although the SP state does not break the SU(2) symmetry
in finite systems, it does so in the thermodynamic limit by making a linear
combination with other states that are degenerate in that limit. We also
calculate the one-particle spectral function and dynamical spin and charge
susceptibilities for various 1D finite-size lattices. We find that the
excitation spectrum of the SP state and the F state is almost identical. Our
present results suggest that the SP and the F states are equivalent in the
thermodynamic limit. These properties may be exploited to determine the
magnetic phase diagram from finite-size studies.
