Exact Partition Function Zeros of a Polymer on a Simple-Cubic Lattice

Abstract

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.

21 pages, 4 figures

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• Solvent-Induced Negative Energetic Elasticity in a Lattice Polymer Chain
• Analytic Partition Function Zeros of the Wako-Saito-Munoz-Eaton beta-hairpin Model
• Finite-size corrections and scaling for the dimer model on the checkerboard lattice
• Energy spectrum of interacting gas: cluster expansion method
• Universal Conductance Fluctuations of Topological Insulators