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Towards field-theoretic simulations with non-invertible pair potentials
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Towards field-theoretic simulations with non-invertible pair potentials

Anh T. Ngo
Master of Science (M.S.), Drexel University
Jun 2025
DOI:
https://doi.org/10.17918/00011037
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Abstract

Field theory Molecular dynamics simulation Polymers
The Lennard-Jones (LJ) potential is a foundational model in molecular dynamics (MD) simulations to represent pairwise interactions, but its singularity at r = 0 makes it unsuitable for direct use in field-theoretic simulations. To address this, a regularized model potential, or Multi-Gaussian potentials, that closely resembles the LJ form is proposed and analyzed within a field-theoretic framework. A perturbative approach based on the Random Phase Approximation (RPA) is developed to derive analytical expressions for the pressure and chemical potential. This approximation scheme is then incorporated into a Gibbs ensemble framework to generate analytical expressions for the chemical potential and pressure. This yields phase coexistence diagrams of the fluid within minutes using Python. The results from RPA are also compared to HOOMD-based MD simulations, with the difference in the osmotic pressure throughout the concentration profile to be 2%. Although discrepancies are observed between the two approaches, the field-theoretic model shows promising qualitative agreement, highlighting its potential as a complementary tool for simulating polymeric systems and soft matter. This work demonstrates a possibility integrating realistic pair potentials into field-theoretic models.

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