Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session X16: Complex Networks
8:00 AM–10:24 AM,
Friday, March 19, 2021
Sponsoring Unit: GSNP
Chair: Kevin Bassler, Univ of Houston
Abstract: X16.00008 : Clusters crossed by a random walk in two-dimensional systems*
9:24 AM–9:36 AM
How many distinct neighborhoods could a walking pedestrian encounter in a city? The naive "area law" expectation suggests a linear scaling of the number of features as a function of path length, so the walker sees more neighborhoods (clusters) as he walks a longer distance. However, interesting phenomena occur when the underlying structure is critical, for sharp turns in the walker's path lead to a universal logarithmic decrease in the cluster count . This observation can be used to detect if the underlying clusters are critical and pinpoint the universality class . Here we consider a random walk with constant, unpredictable turns, leading to an unexplored singular limit that potentially reveals more information about the underlying complex system. Due to the area law, multiplicative poly-logarithmic corrections exist even if the cluster structure is off-critical . We hypothesize a combination of both multiplicative and additive logarithmic corrections for critical clusters and confront this assumption both numerically and analytically.
 Kovacs I.A. et al. PRB 86(2012)214203
 Kovacs I.A. et al. PRB 89(2014)064421
 van Wigland F. et al. J. Phys. A: Math. Gen 30(1996) 507-531
*We would like to acknowledge the Baker Grant from the Weinberg College of Arts and Sciences.
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