Helix-coil transition in terms of Potts-like spins

In the spin model of a helix-coil transition in polypeptides a preferred value of spin has to be assigned to the helical conformation, in order to account for different symmetries of the helical {\sl vs.} the coil states, leading thus to the {\sl Generalized Model of Polypeptide Chain} (GMPC) Hamiltonian as opposed to the Potts model Hamiltonian, both with many-body interactions. Comparison of explicit transfer-matrix secular equations of the Potts model and the GMPC model reveals that the largest eigenvalue of the Potts model with $\Delta$ many-body interactions {\sl coincides} with the largest eigenvalue of the GMPC model with $\Delta-1$ many-body interactions, indicating the identity of both free energies. In distinction, the second largest eigenvalues in both models do {\sl not coincide}, indicating a different behavior for the spatial correlation length that in its turn defines the width of the helix-coil transition interval. We explore in detail the thermodynamic consequences, resulting from spin models with and without the built-in spin anisotropy, that should indicate which model to favour as a more appropriate description of the equilibrium physical properties pertaining to the helix-coil transition