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
Live
Presenter:
Sam Frank
(Northwestern University)
Authors:
Sam Frank
(Northwestern University)
Istvan Kovacs
(Northwestern University)
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 [1]. This observation can be used to detect if the underlying clusters are critical and pinpoint the universality class [2]. 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 [3]. We hypothesize a combination of both multiplicative and additive logarithmic corrections for critical clusters and confront this assumption both numerically and analytically.
[1] Kovacs I.A. et al. PRB 86(2012)214203
[2] Kovacs I.A. et al. PRB 89(2014)064421
[3] 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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