  Helix-coil transition in polypeptides is an example of a spin model with a
preferred spin direction, in the sense that a theoretical formulation of this
problem requires to assign a preferred value of spin to the helical
conformation in order to account for different symmetries of the helical {\sl
vs.} the coil states. This leads to the spin Hamiltonian of the {\sl
Generalized Model of Polypeptide Chain} (GMPC) variety as opposed to the Potts
model variety, both with many-body interactions. We compare the explicit
solution of the Potts model and the solution of the GMPC within the
transfer-matrix formalism. Comparison of both secular equations reveals that
the largest eigenvalue of the Potts model with $\Delta$ many-body interactions
is identical to the largest eigenvalue of the GMPC model with $\Delta-1$
many-body interactions, indicating the equivalence of both free energies. In
distinction, the second largest eigenvalues do not coincide, leading to
different thermal behavior of the spatial correlation length, related to the
helix-coil transition interval. Spin models with built-in spin anisotropy thus
engender different physical properties in the thermodynamic limit that we
explore in detail.

Statistical Mechanics