TY - JOUR
T1 - Finite-size scaling for the glass transition
T2 - The role of a static length scale
AU - Karmakar, Smarajit
AU - Procaccia, Itamar
N1 - European Research Council; Israel Science Foundation; German Israeli FoundationThis work had been supported in part by an advanced "ideas" grant of the European Research Council, the Israel Science Foundation, and the German Israeli Foundation. We thank Shiladitya Sengupta, JNCASR, Bangalore for many useful discussions.
PY - 2012/12/10
Y1 - 2012/12/10
N2 - Over the past 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 supercooled liquid increases by many orders of magnitude upon decreasing the temperature over a modest range. A natural concern in these computer simulations 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 turn this limitation to our advantage by performing finite size scaling on the system size dependence of the relaxation time for supercooled liquids to emphasize the importance of a growing static length scale in the theory of glass transition. We demonstrate that the static length scale that was discovered by us in Physica A0378-437110.1016/j.physa.2011.11.020 391, 1001 (2012) fits the bill extremely well, allowing us to provide a finite-size scaling theory for the α-relaxation time of the glass transition, including predictions for the thermodynamic limit based on simulations in small systems.
AB - Over the past 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 supercooled liquid increases by many orders of magnitude upon decreasing the temperature over a modest range. A natural concern in these computer simulations 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 turn this limitation to our advantage by performing finite size scaling on the system size dependence of the relaxation time for supercooled liquids to emphasize the importance of a growing static length scale in the theory of glass transition. We demonstrate that the static length scale that was discovered by us in Physica A0378-437110.1016/j.physa.2011.11.020 391, 1001 (2012) fits the bill extremely well, allowing us to provide a finite-size scaling theory for the α-relaxation time of the glass transition, including predictions for the thermodynamic limit based on simulations in small systems.
UR - http://www.scopus.com/inward/record.url?scp=84871743750&partnerID=8YFLogxK
U2 - https://doi.org/10.1103/PhysRevE.86.061502
DO - https://doi.org/10.1103/PhysRevE.86.061502
M3 - مقالة
SN - 1539-3755
VL - 86
JO - Physical Review E
JF - Physical Review E
IS - 6
M1 - 061502
ER -