Math-Sci Seminar

Speaker:  Michael Hinczewski, Feza Gürsey Institute, Istanbul, Turkey

Title:  Statistical Mechanics on Complex Networks:Unusual Magnetic Orderings on a Scale-Free, Small-world Hierarchical Lattice

Date: Thu 5 Oct, 2006

Time: 16:45
Place: Science Building, Room Z42

Abstract:

Recent years have seen a surge of interest in complex networks, which can 
describe systems as diverse as traffic on the world-wide web, metabolic 
interactions in cells, and the spread of epidemics among populations. 
From a statistical physics perspective, these networks provide an 
intriguing avenue for tackling one of the long-standing questions in the 
field: how the collective behavior of interacting objects is influenced by 
the topology of those interactions.  In this talk, I will show how 
renormalization-group techniques can yield exact solutions for the Ising 
magnet---the canonical example of cooperative behavior---on a complex 
network.  This network is a novel hierarchical lattice incorporating three 
key features of many real-world systems---a scale-free degree 
distribution, a high clustering coefficient, and the small-world effect. 
By varying the probability p of long-distance bonds, we can study an 
entire spectrum of network structures and the corresponding critical 
behavior.  For large p, where the network exhibits a small-world 
character, we find a highly unusual phase transition: an inverted 
Berezinskii-Kosterlitz-Thouless singularity with infinite correlation 
length and algebraic order in the high-temperature phase.  This is one of 
the few examples of such a singularity where there is no apparent mapping 
of the system onto an XY magnet.  Since most physical interactions decay 
at large separation, we also show how adding distance-dependence to the 
long-range bonds changes the nature of the phase transitions in our 
network.


Please visit http://home.ku.edu.tr/~sci-math for a schedule of
upcoming Science -Math seminars at Koc University.