Universal Amplitude Ratios for Constrained Critical Systems

The critical properties of systems under constraint differ from their ideal counterparts through Fisher renormalization. The mathematical properties of Fisher renormalization applied to critical exponents are well known: the renormalized indices obey the same scaling relations as the ideal ones and the transformations are involutions in the sense that re-renormalizing the critical exponents of the constrained system delivers their original, ideal counterparts. Here we examine Fisher renormalization of critical amplitudes and show that, unlike for critical exponents, the associated transformations are not involutions. However, for ratios and combinations of amplitudes which are universal, Fisher renormalization is involutory.Comment: JSTAT published versio

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.Comment: 16 pages, 6 figures consisting of 16 panels. Presentation and reference list improved for version

The Site-Diluted Ising Model in Four Dimension

In the literature, there are five distinct, fragmented sets of analytic predictions for the scaling behaviour at the phase transition in the random-site Ising model in four dimensions. Here, the scaling relations for logarithmic corrections are used to complete the scaling pictures for each set. A numerical approach is then used to confirm the leading scaling picture coming from these predictions and to discriminate between them at the level of logarithmic corrections.Comment: 15 pages, 5 ps figures. Accepted for publication in Phys. Rev.

The Logarithmic Triviality of Compact QED Coupled to a Four Fermi Interaction

This is the completion of an exploratory study of Compact lattice Quantum Electrodynamics with a weak four-fermi interaction and four species of massless fermions. In this formulation of Quantum Electrodynamics massless fermions can be simulated directly and Finite Size Scaling analyses can be performed at the theory's chiral symmetry breaking critical point. High statistics simulations on lattices ranging from $8^4$ to $24^4$ yield the equation of state, critical indices, scaling functions and cumulants. The measurements are well fit with the orthodox hypothesis that the theory is logarithmically trivial and its continuum limit suffers from Landau's zero charge problem.Comment: 27 pages, 15 figues and 10 table

Scaling and Density of Lee-Yang Zeroes in the Four Dimensional Ising Model

The scaling behaviour of the edge of the Lee--Yang zeroes in the four dimensional Ising model is analyzed. This model is believed to belong to the same universality class as the $\phi^4_4$ model which plays a central role in relativistic quantum field theory. While in the thermodynamic limit the scaling of the Yang--Lee edge is not modified by multiplicative logarithmic corrections, such corrections are manifest in the corresponding finite--size formulae. The asymptotic form for the density of zeroes which recovers the scaling behaviour of the susceptibility and the specific heat in the thermodynamic limit is found to exhibit logarithmic corrections too. The density of zeroes for a finite--size system is examined both analytically and numerically.Comment: 17 pages (4 figures), LaTeX + POSTSCRIPT-file, preprint UNIGRAZ-UTP 20-11-9

Scaling Relations for Logarithmic Corrections

Multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical-mechanical systems. Here, a Lee-Yang zero approach is used to systematically analyse the exponents of such logarithms and to propose scaling relations between them. These proposed relations are then confronted with a variety of results from the literature.Comment: 4 page

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 $\lambda=1$, while for even $\mathcal{N}$ it is infinite ($\lambda=\infty$). 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.Comment: 15 pages, 4 figure

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.Comment: 6 pages, 8 figures, accepted for publication in EP

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, M\"obius 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.Comment: 13 pages. Expanded text with additional result