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

TL;DR

This study analyzes the conformational transitions of a polymer on a simple-cubic lattice by calculating the exact partition function zeros up to chain length 24, revealing insights into phase transitions and scaling behavior.

Contribution

It provides the first exact calculation of partition function zeros for a polymer on a simple cubic lattice, identifying multiple transition loci and their scaling properties.

Findings

Identified two loci of zeros indicating coil-globule and melting transitions.

The coil-globule transition locus approaches the real axis with increasing chain length.

Observed a first-order-like pseudo-transition through specific heat analysis.

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.