The partition function zeros for a Potts model of helix-coil transition with three-site interactions

The partition function (Fisher) zeros of the Q-state Potts model with three-site interactions on a zigzag ladder are studied by a transfer-matrix approach. This Q-state model is proposed as a description of helix-coil transition in homopolymers. The Fisher zeros are exactly derived for arbitrary value of the system parameter Q. It is shown that there is only a quasi-phase transition for all temperatures. The dependence of the helix-coil transition on solvent is analyzed using Fisher zeros of the model. The densities of the Fisher zeros are singular at the edge singularity points and the critical exponent σ=−12.