Finite-size scaling for the glass transition: The role of a static length scale

Karmakar, Smarajit; Procaccia, Itamar

doi:10.1103/physreve.86.061502

Cited by 29 publications

(34 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…140,[152][153][154][155] The size of the system under study can be tuned and finite-size scaling analysis can reveal important lengthscales for the glass problem. 156,157…”

Section: Computer Simulations Of Glass-forming Liquidsmentioning

confidence: 99%

Configurational entropy of glass-forming liquids

Berthier

Ozawa

Scalliet

2019

The Journal of Chemical Physics

View full text Add to dashboard Cite

The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraud with difficulties, misconceptions and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain why the configurational entropy has become a key quantity to describe glassy materials, from early empirical observations to modern theoretical treatments. We explain why practical measurements necessarily require approximations that make its physical interpretation delicate. We then demonstrate that computer simulations have become an invaluable tool to obtain precise, non-ambiguous, and experimentally-relevant measurements of the configurational entropy. We describe a panel of available computational tools, offering for each method a critical discussion. This perspective should be useful to both experimentalists and theoreticians interested in glassy materials and complex systems. I. CONFIGURATIONAL ENTROPY AND GLASS FORMATION A. The glass transitionWhen a liquid is cooled, it can either form a crystal or avoid crystallization and become a supercooled liquid. In the latter case, the liquid remains structurally disordered, but its relaxation time increases so fast that there exists a temperature, called the glass temperature T g , below which structural relaxation takes such a long time that it becomes impossible to observe. The liquid is then trapped virtually forever in one of many possible structurally disordered states: this is the basic phenomenology of the glass transition. 1-4 Clearly, T g depends on the measurement timescale and shifts to lower temperatures for longer observation times. The experimental glass transition is not a genuine phase transition, as it is not defined independently of the observer.The rich phenomenology characterizing the approach to the glass transition has given rise to a thick literature. It is not our goal to review it, and we refer instead to previous articles. 1-9 There are convincing indications that the dynamic slowing down of supercooled liquids is accompanied by an increasingly collective relaxation dynamics. This is seen directly by the measurement of growing lengthscales for these dynamic heterogeneities, 10-12 or more indirectly by the growth of the apparent activation energy for structural relaxation, as seen in its non-Arrhenius temperature dependence. These observations suggest an interpretation of the experimental glass transition in terms of a generic, collective mechanism possibly controlled by a sharp phase transition. 13 'Solving the glass problem' thus amounts to identifying and obtaining direct experimental signatures about the fundamental nature and the mathematical des...

show abstract

“…140,[152][153][154][155] The size of the system under study can be tuned and finite-size scaling analysis can reveal important lengthscales for the glass problem. 156,157…”

Section: Computer Simulations Of Glass-forming Liquidsmentioning

confidence: 99%

Configurational entropy of glass-forming liquids

Berthier

Ozawa

Scalliet

2019

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…[29], it was shown that the length scale obtained via the methods mentioned above for three dimensional systems completely explains the finite size effects seen in the relaxation time τ α for all temperatures including high temperatures. So, for the two dimensional systems, we employed the method of finite-size scaling of τ α [30] to obtain the static length scales as the eigenvalue method and PTS methods involve much larger computational efforts to obtain the length scale. In Fig.1, we have shown the finite-size scaling of τ α to obtain the static length scale for both the two dimensional models.…”

Section: Configurational Entropymentioning

confidence: 99%

Understanding the dynamics of glass-forming liquids with random pinning within the random first order transition theory

Chakrabarty

Das

Karmakar

et al. 2016

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

Extensive computer simulations are performed for a few model glass-forming liquids in both two and three dimensions to study their dynamics when a randomly chosen fraction of particles are frozen in their equilibrium positions. For all the studied systems, we find that the temperaturedependence of the α relaxation time extracted from an overlap function related to the self part of the density autocorrelation function can be explained within the framework of the Random First Order Transition (RFOT) theory of the glass transition. We propose a scaling description to rationalize the simulation results and show that our data for the α relaxation time for all temperatures and pin concentrations are consistent with this description. We find that the fragility parameter obtained from fits of the temperature dependence of the α relaxation time to the Vogel-Fulcher-Tammann (VFT) form decreases by almost an order of magnitude as the pin concentration is increased from zero. Our scaling description relates the fragility parameter to the static length scale of RFOT and thus provides a physical understanding of fragility within the framework of the RFOT theory. Implications of these findings for the values of the exponents appearing in the RFOT theory are discussed.

show abstract

“…[22] and employed further in [23]. The starting point of the second method is the fact that at low frequency the tail of the density of state (DOS) of amorphous solids consisting of N particles reflects the excess of plastic modes which do not exist in the density of states of purely elastic solid [24,25].…”

mentioning

confidence: 99%

Comparison of Static Length Scales Characterizing the Glass Transition

2013

Self Cite

View full text Add to dashboard Cite

The dramatic dynamic slowing down associated with the glass transition is considered by many to be related to the existence of a static length scale that grows when temperature decreases. Defining, identifying and measuring such a length is a subtle and non-trivial problem. Recently, two proposals, based on very different insights regarding the relevant physics, were put forward. One approach is based on the point-to-set correlation technique and the other on the scale where the lowest eigenvalue of the Hessian matrix becomes sensitive to disorder. In this Letter we present numerical evidence that the two approaches might result in the same identical length scale. This provides further mutual support to their relevance and, at the same time, raise interesting theoretical questions, discussed in the conclusion, concerning the fundamental reason for their relationship.A natural assumption that prevails in the physics community regarding the glass transition is that together with the spectacular slowing down associated with this phenomenon there should be also a length scale that increases in accordance with the increased time scale [1]. Decades of research efforts were devoted to find such a length [2,3]. The discovery of dynamic heterogeneity in super-cooled liquids both in experiments and in theoretical studies [4] and the detailed analysis of the associated dynamical length-scale using multi-point correlation functions [5][6][7][8][9][10][11][12] revealed that more and more particles move in a correlated way approaching the glass transition. There is no doubt by now that there exists a growing dynamic length accompanying the glass transition. Although this is a new and important facet of the phenomenology of super-cooled liquids, it is still not clear to what extent dynamic correlations are the consequence or the primary origin of slow dynamics [11]. Another natural candidate for the dominant length-scale of glassy dynamics is a static length. Finding it remained an open problem for a long time. Recently, two very specific and very different methods to determine the elusive characteristic length scales had been proposed and implemented. In this Letter we review both methods and provide numerical indications that although the two methods are extremely different, they seem to lead to the same length scale. This provides further mutual support to their relevance and, at the same time, raises interesting theoretical questions concerning the fundamental reason for their relationship.The first method is based on the "point-to-set" (PTS) length [13,14] that will denote henceforth as ξ PTS . This length, originally introduced to characterize the real space structure of the so called "mosaic state" arising in the Random First Order Transition theory [13,15], allows one to probe the spatial extent of positional amorphous order. It has attracted a lot of attention recently. In particular, it was measured in several numerical simulations [16][17][18][19][20] and shown to grow mildly in the (rather high) temperature regime ...

show abstract

Finite-size scaling for the glass transition: The role of a static length scale

Cited by 29 publications

References 39 publications

Configurational entropy of glass-forming liquids

Configurational entropy of glass-forming liquids

Understanding the dynamics of glass-forming liquids with random pinning within the random first order transition theory

Comparison of Static Length Scales Characterizing the Glass Transition

Contact Info

Product

Resources

About