Pole Analysis of the Inter-Replica Correlation Function in a Two-Replica System as a Binary Mixture: Mean Overlap in the Cluster Glass Phase

TL;DR

This paper analyzes the inter-replica correlation function in a two-replica system to understand the cluster glass phase of ultrasoft particles, deriving an analytical formula for the mean overlap that explains numerical observations.

Contribution

It introduces a pole analysis approach combined with a hierarchical free-energy landscape view to derive an analytical expression for the mean overlap in the cluster glass phase.

Findings

Derived an analytical formula for mean overlap in the cluster glass phase.

Connected pole analysis with numerical findings in the Gaussian core model.

Provided insights into the free-energy landscape of the system.

Abstract

To investigate the cluster glass phase of ultrasoft particles, we examine an annealed two-replica system endowed with an attractive inter-replica field similar to that of a binary symmetric electrolyte. Leveraging this analogy, we conduct pole analysis on the total correlation functions in the two-replica system where the inter-replica field will eventually be switched off. By synthesizing discussions grounded in the pole analysis with a hierarchical view of the free-energy landscape, we derive an analytical form of the mean overlap between two replicas within the mean field approximation of the Gaussian core model. This formula elucidates novel numerical findings observed in the cluster glass phase.