Parallel Algorithm for Calculation of the Exact Partition Function of a Lattice Polymer

TL;DR

This paper introduces a parallel algorithm to compute the exact partition function of lattice polymers efficiently, enabling detailed thermodynamic analysis of polymer collapse transitions for chains up to length 36.

Contribution

A novel parallel algorithm that classifies conformations by shape to efficiently compute the partition function of lattice polymers, reducing redundant calculations.

Findings

Successfully computed the specific heat for chain length 36.

Demonstrated efficient parallelization reducing computation time.

Provided insights into the collapse transition of lattice homopolymers.

Abstract

We develop a parallel algorithm that calculates the exact partition function of a lattice polymer, by enumerating the number of conformations for each energy level. An efficient parallelization of the calculation is achieved by classifying the conformations according to the shape of the box spanned by a conformation, and enumerating only those in a given box at a time. The calculation time for each box is reduced by preventing the conformations related by symmetries from being generated more than once. The algorithm is applied to study the collapse transition of a lattice homopolymer on a square lattice, by calculating the specific heat for chain lengths up to 36.