Structural changes in the Lennard-Jones supercooled liquid and ideal glass: an improved integral equation for the replica method

Framing the glass formation within standard statistical mechanics is an outstanding problem of condensed matter theory. To provide new insight, we investigate the structural properties of the Lennard-Jones fluid in the very-low temperature regime, by using a replicated version of the refined HMSA theory of the liquid state, combined with an appropriate split of the pair potential [Bomont and Bretonnet, J. Chem. Phys. 114, 4141 (2001)]. Our scheme allows one to reach an unprecedented low-temperature domain within both the supercooled liquid and the ideal-glass phase. Therein, a density-dependent temperature is identified, whereupon the radial distribution function experiences clear-cut structural changes, insofar as an additional peak develops in between the main and the second peaks. Such a structural feature points to a local structure of the Lennard-Jones ideal glass with an fcc-like short-range order, in the absence of any long-range order.

💡 Research Summary

The paper tackles one of the most challenging problems in condensed‑matter physics: describing glass formation within the framework of equilibrium statistical mechanics. The authors focus on the Lennard‑Jones (LJ) fluid, extending its study to temperatures far below those accessible by conventional simulation techniques. To achieve this, they combine a replicated version of the refined hybridized‑mean‑spherical‑approximation (R‑HMSA) with an Optimized Division Scheme (ODS) for splitting the LJ pair potential into short‑range (reference) and long‑range (perturbative) parts.

In the replica approach, two identical copies (replicas) of the system, each containing N particles, interact via the usual LJ potential within each replica (u₁₁ = u₂₂ = u) and via a weak, short‑range attractive potential u₁₂(r) = –ε₁₂ w(r) between replicas. The coupling constant ε₁₂ is taken to zero after the calculation, allowing the definition of an overlap order parameter Q = 8πρ∫₀^∞ g₁₂(r) w(r) r² dr, where g₁₂(r) is the inter‑replica radial distribution function. Q and the value g₁₂(0) serve as diagnostics for the Random First‑Order Transition (RFOT) scenario: at high temperature the replicas are decoupled (Q = Q_random, g₁₂(0)=1), while upon cooling both quantities increase, signalling the emergence of a glassy phase.

The HMSA closure employed reads
g_ij(r) = exp