Computation of the Complexity of the Disordered Liquid: A Replica Field Approach

Prakash Vardhan, Trideep Rajbhar

Abstract: The configurational entropy, or complexity, of disordered liquids a fundamental quantity governing the glass transition?remains poorly understood due to the challenges of quantifying metastable states in systems with self-generated disorder. This paper presents a replica field theory framework to compute the complexity of disordered liquids, adapting methods originally developed for spin glasses to address the unique features of amorphous materials. By treating the liquid's density fluctuations as an emergent quenched disorder field, we derive an effective action that encodes the interplay between thermal fluctuations and metastable states. Utilizing Parisi's replica symmetry breaking (RSB) scheme, we solve the saddle-point equations to obtain the complexity as a function of temperature and density. Our results reveal a critical temperature TKTK at which the complexity vanishes, signaling an ideal glass transition characterized by a power-law divergence ??(T?TK)?, with ??1.5 in three dimensions. The theory reconciles key predictions of random first-order transition (RFOT) theory, including the Kauzmann temperature and hierarchical state organization, while highlighting limitations of mode-coupling theory (MCT) at low temperatures. Comparisons with molecular dynamics simulations of Lennard-Jones liquids confirm the universality of the derived scaling behavior. This work establishes a rigorous connection between replica-based approaches and the statistical mechanics of liquids, offering a pathway to explore non-equilibrium dynamics, anisotropic interactions, and experimental signatures of configurational entropy in glass-forming systems.

Keywords: replica field theory, saddle-point equations, power-law divergence, random first-order transition, statistical mechanics of liquids

How to Cite?: Prakash Vardhan, Trideep Rajbhar, "Computation of the Complexity of the Disordered Liquid: A Replica Field Approach", Volume 14 Issue 5, May 2025, International Journal of Science and Research (IJSR), Pages: 554-557, https://www.ijsr.net/getabstract.php?paperid=SR25506192804, DOI: https://dx.doi.org/10.21275/SR25506192804