Finite Size Scaling for the Glass Transition: the Role of a Static Length Scale

TL;DR

This paper develops a finite size scaling theory for the glass transition based on a static length scale, enabling predictions of bulk behavior from small system simulations.

Contribution

It introduces a finite size scaling framework for the glass transition utilizing a static length scale, bridging small simulations and thermodynamic limit predictions.

Findings

The static length scale from previous studies fits the finite size scaling theory well.

The theory predicts how the alpha relaxation time scales with system size and temperature.

It provides a method to infer bulk properties from small-scale simulations.

Abstract

Over the last decade computer simulations have had an increasing role in shedding light on difficult statistical physical phenomena and in particular on the ubiquitous problem of the glass transition. Here in a wide variety of materials the viscosity of a super-cooled liquid increases by many orders of magnitude upon decreasing the temperature over a modest range. A natural concern in these computer simulation is the very small size of the simulated systems compared to experimental ones, raising the issue of how to assess the thermodynamic limit. Here we offer a theory for the glass transition based on finite size scaling, a method that was found very useful in the context of critical phenomena and other interesting problems. As is known, the construction of such a theory rests crucially on the existence of a growing {\em static} length scale upon decreasing the temperature. We demonstrate that the static length scale that was discovered in Ref. \cite{12KLP} fits the bill extremely well, allowing us to provide a finite size scaling theory for the $\alpha$ relaxation time of the glass transition, including predictions for the thermodynamic limit based on simulations in small systems.