TY - JOUR

T1 - Modified facilitated kinetic Ising model for supercooled liquids

AU - Halpern, V.

PY - 2000/5/15

Y1 - 2000/5/15

N2 - A modification is considered of the well-known Fredrickson-Andersen facilitated kinetic Ising model for studying the glass transition in supercooled liquids. In this modification, which we call the cluster facilitated kinetic Ising model (CluFKI) model, the flip of a spin between the liquid-like regions represented by A or up states and the solid-like regions represented by B or down states can occur (i.e. is facilitated) only if in the cluster containing the spin and those adjacent to it there are at least n spins in the A state. As a result, the transition from a solid-like to a liquid-like region requires more free volume than the reverse transition, which is physically very reasonable. Computer calculations for the n = 1 CluFKI model, as well as a qualitative analysis, show that as the temperature T of the system decreases, and so the parameter x = E/T increases, the fraction fA of spins in state A when the system is in a metastable steady state decreases until it reaches zero for a critical value xc. Correspondingly, the mean relaxation time 〈τ〉 of the system's memory function increases rapidly, and 〈τ〉→∞ as x→xc. This behaviour is similar to that for the α-relaxation in supercooled liquids as the glass transition temperature is approached.

AB - A modification is considered of the well-known Fredrickson-Andersen facilitated kinetic Ising model for studying the glass transition in supercooled liquids. In this modification, which we call the cluster facilitated kinetic Ising model (CluFKI) model, the flip of a spin between the liquid-like regions represented by A or up states and the solid-like regions represented by B or down states can occur (i.e. is facilitated) only if in the cluster containing the spin and those adjacent to it there are at least n spins in the A state. As a result, the transition from a solid-like to a liquid-like region requires more free volume than the reverse transition, which is physically very reasonable. Computer calculations for the n = 1 CluFKI model, as well as a qualitative analysis, show that as the temperature T of the system decreases, and so the parameter x = E/T increases, the fraction fA of spins in state A when the system is in a metastable steady state decreases until it reaches zero for a critical value xc. Correspondingly, the mean relaxation time 〈τ〉 of the system's memory function increases rapidly, and 〈τ〉→∞ as x→xc. This behaviour is similar to that for the α-relaxation in supercooled liquids as the glass transition temperature is approached.

UR - http://www.scopus.com/inward/record.url?scp=0033733134&partnerID=8YFLogxK

U2 - 10.1088/0953-8984/12/19/301

DO - 10.1088/0953-8984/12/19/301

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AN - SCOPUS:0033733134

SN - 0953-8984

VL - 12

SP - 4303

EP - 4311

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

IS - 19

ER -