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Helix-coil transition in polypeptides is an example of a spin model with apreferred spin direction, in the sense that a theoretical formulation of thisproblem requires to assign a preferred value of spin to the helicalconformation in order to account for different symmetries of the helical {\slvs.} the coil states. This leads to the spin Hamiltonian of the {\slGeneralized Model of Polypeptide Chain} (GMPC) variety as opposed to the Pottsmodel variety, both with many-body interactions. We compare the explicitsolution of the Potts model and the solution of the GMPC within thetransfer-matrix formalism. Comparison of both secular equations reveals thatthe largest eigenvalue of the Potts model with $\Delta$ many-body interactionsis identical to the largest eigenvalue of the GMPC model with $\Delta-1$many-body interactions, indicating the equivalence of both free energies. Indistinction, the second largest eigenvalues do not coincide, leading todifferent thermal behavior of the spatial correlation length, related to thehelix-coil transition interval. Spin models with built-in spin anisotropy thusengender different physical properties in the thermodynamic limit that weexplore in detail.

One dimensional Potts model with many-body interactions and the Generalized Model of Polypeptide Chain for the helix-coil transition