Ralph Kenna

In statistical physics, Kenna is noted for his development of scaling relations for logarithmic corrections.[8][9] Already in his PhD Thesis[10] he introduced a renormalization group basis for finite-size scaling (FSS) for logarithmic corrections at the upper critical dimension and, with Bertrand Berche, he extended this to higher dimensions in 2012.[11] They proposed that universality lives at the pseudocritical point instead of at the critical point and a new form for hyperscaling, valid in high dimensions.[11] This led to the introduction of the new critical exponent ϙ (koppa) and its logarithmic counterpart ϙ̂ (ϙ-hat or koppa-hat)[12] to govern the finite-size dependence of the correlation length and a new form for FSS, called QFSS,[13] to replace standard prescription above the upper critical dimension. Fourier analysis showed two regimes that control finite systems in high dimensions instead of Landau scaling.[14] The Q sector is affected by dangerous irrelevant variables and the Gaussian, or G, sector (G) is not but both are physical. The pseudocritical point resides in the Q sector while the critical point itself may be either Q or G.[15]

Formal similarities between spin systems on lattices and on scale-free networks mean an analogy between dimensionality and power-law decay of the node degree distribution there. Logarithmic corrections at critical values[16][17] also obey the scaling relations developed by Kenna in 2006.[8][9] Kenna's work on percolation theory in high dimensions and spin models on annealed scale-free networks has featured in the Institute of Physics News.[18][19]

In 2010, with Bertrand Berche, Kenna quantified the notion of critical mass of academic research groups.[20] Using data from the UK's Research Assessment Exercise 2008 and the French counterpart (AERES) they tracked how research group quality depends on the size of the group.[21][22][23] They found quality rises linearly with group size up to a point which they later identified as akin to the Dunbar number in anthropology. Critical mass, defined as the minimum size a group needs to achieve to be sustainable, is half that size.[24] Subsequently, with Olesya Mryglod and Yurij Holovatch, Kenna and Berche used scientometrics to predict the outcome of the UK's Research Excellence Framework 2014.[25][26] They found that correlations between metrics and peer review are poor and the former cannot reliably be used to replace the latter.[27] This went some way to halting the overuse of metrics at the Research Excellence Framework 2021.[28][29][30][31]

In comparative mythology Kenna is noted for pioneering the usage of complex networks in the study of Irish and other mythologies. His first paper[32] on the topic was downloaded over 30,000 times in 10 years, a record [33] for Europe's flagship letters journal in physics, and resulted in considerable media coverage in international press.[34][35][36][37][38][39][40] Other major works include investigations into the Sagas of Icelanders.[41] Kenna's team found that whether the sagas are historically accurate or not, the properties of the social worlds they record are similar to those of real social networks.[42][43][44][45][46][47] The epic poems of Ossian[48] were the focus of the next subject of study with conclusions broadly in line with the view they were misappropriated from Irish sources.[49][50] The Viking Age in Ireland as portrayed in Cogadh Gaedhel re Gallaibh was next tackled by Kenna's team.[51] They developed a measure to place hostility on a spectrum between civil war and international conflict. Their findings[52][53][54][55][56][57] quantified and supported the traditional view of the Viking age in Ireland as one of international conflict and challenged recent revisionist claims. A study of the character Fraoch identified quantifiable differences between the two parts of his story, supporting the suggestion it was set to writing by two different scribes, one of whom embellished the tale.[58] Kenna and co-workers also studied Ukrainian mythology. They compared the Kyiv bylyny cycle to other prominent European epics to identify universal and distinguishing properties of its social networks.[59] Kenna's team developed mathematical and statistical methods to probe how a modern complex narrative - namely George R. R. Martin's epic novels, A Song of Ice and Fire - achieved broad acclaim without surrendering to the need for reductionist simplifications.[60] This and other works on narratology led to sustained media interest.[61][62][63][64]