Related Experiment Video
Updated: Jun 8, 2026

Spatial Separation of Molecular Conformers and Clusters
Published on: January 9, 2014
Exact partition function zeros and the collapse transition of a two-dimensional lattice polymer
Jae Hwan Lee1, Seung-Yeon Kim, Julian Lee
1Department of Bioinformatics and Life Science and School of Systems Biomedical Science, Soongsil University, Seoul 156-743, Korea.
Abstract:
We study the collapse transition of the lattice homopolymer on a square lattice by calculating the exact partition function zeros. The exact partition function is obtained by enumerating the number of possible conformations for each energy value, and the exact distributions of the partition function zeros are found in the complex temperature plane by solving a polynomial equation. We observe that the locus of zeros closes in on the positive real axis as the chain length increases, providing the evidence for the onset of the collapse transition. By analyzing the scaling behavior of the first zero with the polymer length, we estimate the transition temperature T(θ) and the crossover exponent φ.
Related Concept Videos
Phase Transitions: Melting and Freezing
Polymer Classification: Crystallinity
Crystalline domains are the regions where polymer chains are aligned in an orderly manner and held together in proximity by intermolecular forces. For example, chains in the crystalline domains of polyethylene and nylon are bound together by van der Waals...
Phase Transitions: Sublimation and Deposition
Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Structures of Solids
Lattice Centering and Coordination Number
Types of Unit Cells
Imagine taking a large number of identical...

