Replicated liquid theory in 1+∞ dimensions

2025/08/29 by Tomita, Yukihiro, Yoshino, Hajime · 1 citation
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2508.21639

Abstract

We develop a replicated liquid theory for structural glasses which exhibit spatial variation of physical quantities along one axis, say z-axis. The theory becomes exact with infinite transverse dimension d-1 → ∞. It provides an exact free-energy functional with space-dependent glass order parameter Δ_ab(z). As a first application of the scheme, we study diverging lengths associated with dynamic/static glass transitions of hardspheres with/without confining cavity. The exponents agree with those obtained in previous studies on related mean-field models. Moreover, it predicts a non-trivial spatial profile of the glass order parameter Δ_ab(z) within the cavity which exhibits a scaling feature approaching the dynamical glass transition.

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