arXiv subjects

Ralph Kenna

Publications and source records attributed to Ralph Kenna.

At least 55 records · Page 3Linked to original sources

arXiv2014

Is your EPL attractive? Classification of publications through download statistics

Here we consider the download statistics of EPL publications. We find that papers in the journal are characterised by fast accumulations of downloads during the first couple of months after publication, followed by slower rates thereafter, behaviour which can be represented by a model with predictive power. We also find that individual papers can be classified in various ways, allowing us to compare categories for open-access and non-open-access papers. For example, for the latter publications, which comprise the bulk of EPL papers, a small proportion (2%) display intense bursts of download activity, possibly following an extended period of less remarkable behaviour. About 18% have an especially high degree of attractiveness over and above what is typical for the journal. One can also classify the ageing of attractiveness by examining download half-lives. Approximately 18% have strong interest initially, waning in time. A further 20% exhibit "delayed recognition" with relatively late spurs in download activity. Although open-access papers enjoy more downloads on average, the proportions falling into each category are similar.

cs.DL↗

arXiv2014

Comparison of methods to determine point-to-point resistance in nearly rectangular networks with application to a hammock network

Considerable progress has recently been made in the development of techniques to exactly determine two-point resistances in networks of various topologies. In particular, two types of method have emerged. One is based on potentials and the evaluation of eigenvalues and eigenvectors of the Laplacian matrix associated with the network or its minors. The second method is based on a recurrence relation associated with the distribution of currents in the network. Here, these methods are compared and used to determine the resistance distances between any two nodes of a network with topology of a hammock.

math-ph↗

arXiv2014

Exact finite-size corrections for the spanning-tree model under different boundary conditions

We express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions (free, cylindrical, toroidal, Möbius strip, and Klein bottle) in terms of a principal partition function with twisted boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the logarithm of the partition function for each case. We have also established several groups of identities relating spanning-tree partition functions for the different boundary conditions. We also explain an apparent discrepancy between logarithmic correction terms in the free energy for a two dimensional spanning tree model with periodic and free boundary conditions and conformal field theory predictions. We have obtain corner free energy for the spanning tree under free boundary conditions in full agreement with conformal field theory predictions.

cond-mat.stat-mech↗

arXiv2014

Critical Phenomena for Systems under Constraint

It is well known that the imposition of a constraint can transform the properties of critical systems. Early work on this phenomenon by Essam and Garelick, Fisher, and others, focused on the effects of constraints on the leading critical exponents describing phase transitions. Recent work extended these considerations to critical amplitudes and to exponents governing logarithmic corrections in certain marginal scenarios. Here these old and new results are gathered and summarised. The involutory nature of the transformations between the critical parameters describing ideal and constrained systems are also discussed, paying particular attention to matters relating to universality.

cond-mat.stat-mech↗

arXiv2014

Exact asymptotic expansion for the resistance between center node and a node on the cobweb network boundary

We analyze the resistance between two notes in a cobweb network of resistors. Based on an exact expression, we derive the asymptotic expansions for the resistance between the center node and a node on the boundary of the M by N cobweb network of resistors with resistors r and s in the two spatial directions. All coefficients in this expansion are expressed through analytical functions.

cond-mat.stat-mech↗

arXiv2014

Exact finite-size corrections and corner free energies for the c=-2 universality class

We consider (a) the partition functions of the anisotropic dimer model on the rectangular (2M-1) x (2N-1) lattice with free and cylindrical boundary conditions with a single monomer residing on the boundary and (b) the partition function of the anisotropic spanning tree on an M x N rectangular lattice with free boundary conditions. We express (a) and (b) in terms of a principal partition function with twisted boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the free energy for both cases (a) and (b). We confirm the conformal field theory prediction for the corner free energy of these models, and find the central charge is c = - 2. We also show that the dimer model on the cylinder with an odd number of sites on the perimeter exhibits the same finite-size corrections as on the plane.

cond-mat.stat-mech↗

arXiv2014

Hyperscaling above the upper critical dimension

Above the upper critical dimension, the breakdown of hyperscaling is associated with dangerous irrelevant variables in the renormalization group formalism at least for systems with periodic boundary conditions. While these have been extensively studied, there have been only a few analyses of finite-size scaling with free boundary conditions. The conventional expectation there is that, in contrast to periodic geometries, finite-size scaling is Gaussian, governed by a correlation length commensurate with the lattice extent. Here, detailed numerical studies of the five-dimensional Ising model indicate that this expectation is unsupported, both at the infinite-volume critical point and at the pseudocritical point where the finite-size susceptibility peaks. Instead the evidence indicates that finite-size scaling at the pseudocritical point is similar to that in the periodic case. An analytic explanation is offered which allows hyperscaling to be extended beyond the upper critical dimension.

cond-mat.stat-mech↗

arXiv2012

Universal Properties of Mythological Networks

As in statistical physics, the concept of universality plays an important, albeit qualitative, role in the field of comparative mythology. Here we apply statistical mechanical tools to analyse the networks underlying three iconic mythological narratives with a view to identifying common and distinguishing quantitative features. Of the three narratives, an Anglo-Saxon and a Greek text are mostly believed by antiquarians to be partly historically based while the third, an Irish epic, is often considered to be fictional. Here we show that network analysis is able to discriminate real from imaginary social networks and place mythological narratives on the spectrum between them. Moreover, the perceived artificiality of the Irish narrative can be traced back to anomalous features associated with six characters. Considering these as amalgams of several entities or proxies, renders the plausibility of the Irish text comparable to the others from a network-theoretic point of view.

physics.soc-ph↗

arXiv2012

Universal scaling relations for logarithmic-correction exponents

By the early 1960's advances in statistical physics had established the existence of universality classes for systems with second-order phase transitions and characterized these by critical exponents which are different to the classical ones. There followed the discovery of (now famous) scaling relations between the power-law critical exponents describing second-order criticality. These scaling relations are of fundamental importance and now form a cornerstone of statistical mechanics. In certain circumstances, such scaling behaviour is modified by multiplicative logarithmic corrections. These are also characterized by critical exponents, analogous to the standard ones. Recently scaling relations between these logarithmic exponents have been established. Here, the theories associated with these advances are presented and expanded and the status of investigations into logarithmic corrections in a variety of models is reviewed.

cond-mat.stat-mech↗

arXiv2011

The dimer model on the triangular lattice

We analyze the partition function of the dimer model on an $\mathcal{M} \times \mathcal{N}$ triangular lattice wrapped on torus obtained by Fendley, Moessner and Sondhi [Phys. Rev. B \textbf{66}, 214513 (2002)]. From a finite-size analysis we have found that the dimer model on such a lattice can be described by conformal field theory having central charge $c=1$. The shift exponent for the specific heat is found to depend on the parity of the number of lattice sites $\mathcal{N}$ along a given lattice axis: e.g., for odd $\mathcal{N}$ we obtain the shift exponent $λ=1$, while for even $\mathcal{N}$ it is infinite ($λ=\infty$). In the former case, therefore, the finite-size specific-heat pseudocritical point is size dependent, while in the latter case, it coincides with the critical point of the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2011

Scaling behaviour of lattice animals at the upper critical dimension

We perform numerical simulations of the lattice-animal problem at the upper critical dimension d=8 on hypercubic lattices in order to investigate logarithmic corrections to scaling there. Our stochastic sampling method is based on the pruned-enriched Rosenbluth method (PERM), appropriate to linear polymers, and yields high statistics with animals comprised of up to 8000 sites. We estimate both the partition sums (number of different animals) and the radii of gyration. We re-verify the Parisi-Sourlas prediction for the leading exponents and compare the logarithmic-correction exponents to two partially differing sets of predictions from the literature. Finally, we propose, and test, a new Parisi-Sourlas-type scaling relation appropriate for the logarithmic-correction exponents.

cond-mat.stat-mech↗

arXiv2011

Statistics of statisticians: Critical mass of statistics and operational research groups in the UK

Using a recently developed model, inspired by mean field theory in statistical physics, and data from the UK's Research Assessment Exercise, we analyse the relationship between the quality of statistics and operational research groups and the quantity researchers in them. Similar to other academic disciplines, we provide evidence for a linear dependency of quality on quantity up to an upper critical mass, which is interpreted as the average maximum number of colleagues with whom a researcher can communicate meaningfully within a research group. The model also predicts a lower critical mass, which research groups should strive to achieve to avoid extinction. For statistics and operational research, the lower critical mass is estimated to be 9 $\pm$ 3. The upper critical mass, beyond which research quality does not significantly depend on group size, is about twice this value.

math.ST↗

arXiv2011

Normalization of peer-evaluation measures of group research quality across academic disciplines

Peer-evaluation based measures of group research quality such as the UK's Research Assessment Exercise (RAE), which do not employ bibliometric analyses, cannot directly avail of such methods to normalize research impact across disciplines. This is seen as a conspicuous flaw of such exercises and calls have been made to find a remedy. Here a simple, systematic solution is proposed based upon a mathematical model for the relationship between research quality and group quantity. This model manifests both the Matthew effect and a phenomenon akin to the Ringelmann effect and reveals the existence of two critical masses for each academic discipline: a lower value, below which groups are vulnerable, and an upper value beyond which the dependency of quality on quantity reduces and plateaus appear when the critical masses are large. A possible normalization procedure is then to pitch these plateaus at similar levels. We examine the consequences of this procedure at RAE for a multitude of academic disciplines, corresponding to a range of critical masses.

physics.soc-ph↗

arXiv2010

Critical mass and the dependency of research quality on group size

Academic research groups are treated as complex systems and their cooperative behaviour is analysed from a mathematical and statistical viewpoint. Contrary to the naive expectation that the quality of a research group is simply given by the mean calibre of its individual scientists, we show that intra-group interactions play a dominant role. Our model manifests phenomena akin to phase transitions which are brought about by these interactions, and which facilitate the quantification of the notion of critical mass for research groups. We present these critical masses for many academic areas. A consequence of our analysis is that overall research performance of a given discipline is improved by supporting medium-sized groups over large ones, while small groups must strive to achieve critical mass.

physics.soc-ph↗

arXiv2010

The extensive nature of group quality

We consider groups of interacting nodes engaged in an activity as many-body, complex systems and analyse their cooperative behaviour from a mean-field point of view. We show that inter-nodal interactions rather than accumulated individual node strengths dominate the quality of group activity, and give rise to phenomena akin to phase transitions, where the extensive relationship between group quality and quantity reduces. The theory is tested using empirical data on quantity and quality of scientific research groups, for which critical masses are determined.

physics.soc-ph↗

arXiv2010

Concentration versus dispersion of research resources: a contribution to the debate

Using the results of the UK's research assessment exercise, we show that the size or mass of research groups, rather than individual caliber or prestige of the institution, is the dominant factor which drives the quality of research teams. There are two critical masses in research: a lower one, below which teams are vulnerable and an upper one, above which average dependency of research quality on team size reduces. This leveling off refutes arguments which advocate ever increasing concentration of research support into a few large institutions. We also show that to increase research quality, policies which nourish two-way communication links between researchers are paramount.

physics.soc-ph↗

arXiv2009

Critical phenomena: 150 years since Cagniard de la Tour

Critical phenomena were discovered by Cagniard de la Tour in 1822, who died 150 years ago. In order to mark this anniversary, the context and the early history of his discovery is reviewed. We then follow with a brief sketch of the history of critical phenomena, indicating the main lines of development until the present date. Os fenómenos cr\'ıticos foram descobertos pelo Cagniard de la Tour em Paris em 1822. Para comemorar os 150 anos da sua morte, o contexto e a história initial da sua descoberta é contada. Conseguimos com uma descrição breve da história dos fenémenos cr\'ıticos, indicando as linhas principais do desenvolvimento até o presente.

physics.hist-ph↗

arXiv2008

Fisher Renormalization for Logarithmic Corrections

For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogs. The scheme is tested in lattice animals and the Yang-Lee problem at their upper critical dimensions, where predictions for logarithmic corrections are made.

cond-mat.stat-mech↗