  We study conformational transitions of a polymer on a simple-cubic lattice by
calculating the zeros of the exact partition function, up to chain length 24.
In the complex temperature plane, two loci of the partition function zeros are
found for longer chains, suggesting the existence of both the coil-globule
collapse transition and the melting-freezing transition. The locus
corresponding to coil-globule transition clearly approaches the real axis as
the chain length increases, and the transition temperature could be estimated
by finite-size scaling. The form of the logarithmic correction to the scaling
of the partition function zeros could also be obtained. The other locus does
not show clear scaling behavior, but a supplementary analysis of the specific
heat reveals a first-order-like pseudo-transition.
