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New Developments in Critical Phenomena (Hyperscaling) and Complexity (Analysis of Mythological Epics)

Ralph Kenna, University of Coventry

Two very different directions of research are presented. The first concerns the mathematics and statistical physics of critical phenomena. The standard picture is that above the upper critical dimension, hyperscaling fails, finite-size scaling is non-universal, and the anomalous dimension vanishes. We show that these statements are incorrect or incomplete and the (necessary) introduction of a new critical exponent remedies each of these anomalies there.

The second part of the talk contains an unusual application of network theory which has made a lot of media impact recently. Mythological epics frequently entail multitudes of characters in timeless narratives beyond documented history. We study the networks of characters appearing in different mythological narratives, epics and sagas: Beowulf (England), the Iliad (Greece), the Íslendingasögur (Iceland) and the Táin Bó Cúailnge (Ireland), amongst others. By comparing these amongst each other, and to real, fictitious and random networks, we seek to develop a new, quantitative approach to comparative mythology. In particular, we find that each of the societies depicted has, to varying degrees, properties akin to those of real social networks. This quantitative approach forms a basis upon which one may speculate as to the extent to which these narratives may be based upon real or imaginary societies.