arXiv subjects

Ralph Kenna

Publications and source records attributed to Ralph Kenna.

At least 19 recordsLinked to original sources

arXiv2025

Quantum Entanglement Generation in the Heterometallic Ni$^\text{2+}_4$Gd$_4^\text{3+}$ Complexes

We investigate various types of quantum entanglement in the octanuclear heterometallic $3d/4f$ complexes denoted as Ni$^{2+}_4$Gd$^{3+}_4$ under an external magnetic field, using the exact diagonalization approach. These molecular magnets, which can be effectively described by Heisenberg spin models, consist of two identical $\{\text{Ni}^{2+}_2\text{Gd}^{3+}_2\}$ cubane subunits bridged by acetate and hydroxide ligands. Our analysis reveals that their magnetization exhibits intermediate plateaus at low temperatures, indicating distinct ground states characteristic of Ni-containing compounds. Using negativity as a measure of quantum entanglement, we examine the influence of single-ion anisotropy and magnetic field on tetrapartite, bipartite, 1$-$3 tangle, and 2$-$2 tangle entanglements in two families of Ni$^{2+}_4$Gd$^{3+}_4$ complexes: $\boldsymbol{(1)}$ without anisotropy and $\boldsymbol{(2)}$ with anisotropy. Complex $\boldsymbol{(1)}$ exhibits strong bipartite entanglement between Ni ions, which persists up to $T \approx 3.0\,\text{K}$ and $B \approx 4.0\,\text{T}$, but shows significantly weaker tetrapartite entanglement and vanishing bipartite entanglement between Gd$\cdots$Gd and Ni$\cdots$Gd pairs. In contrast, complex $\boldsymbol{(2)}$ displays nonzero and sizable values for all types of entanglement considered. These findings emphasis the crucial role of single-ion anisotropy in generating and shaping the entanglement landscape of heterometallic Ni$^{2+}_4$Gd$^{3+}_4$ complexes. Notably, we find that the 1$-$3 tangle entanglement between a Ni ion and the remaining sites in a cubane unit serves as a reliable indicator of ground-state phase transitions, exhibiting distinct changes across phase boundaries irrespective of the presence of single-ion anisotropy.

cond-mat.mtrl-sci↗

arXiv2025

Partition function zeros for the Blume-Capel model on a complete graph

In this paper we study finite-size effects in the Blume-Capel model through the analysis of the zeros of the partition function. We consider a complete graph and make use of the behaviour of the partition function zeros to elucidate the crossover from effective to asymptotic properties. While in the thermodynamic limit the exact solution yields the asymptotic mean-field behaviour, for finite system sizes an effective critical behaviour is observed. We show that even for large systems, the criticality is not asymptotic. We also present insights into how partition function zeros in different complex fields (temperature, magnetic field, crystal field) give different precision and provide us with different parts of the larger picture. This includes the differences between criticality and tricriticality as seen through the lens of Fisher, Lee-Yang, and Crystal Field zeros.

cond-mat.stat-mech↗

arXiv2024

Scaling and Finite-Size Scaling above the Upper Critical Dimension

In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a fundamental level through the renormalization group. They have been verified in multitudes of theoretical, computational and experimental studies and are firmly established and profoundly important for our understanding of critical phenomena. One of the scaling relations, hyperscaling, fails above the upper critical dimension. There, critical phenomena are governed by Gaussian fixed points in the renormalization-group formalism. Dangerous irrelevant variables are required to deliver the mean-field and Landau values of the critical exponents, which are deemed valid by the Ginzburg criterion. Also above the upper critical dimension, the standard picture is that, unlike for low-dimensional systems, finite-size scaling is non-universal. Here we report on new developments which indicate that the current paradigm is flawed and incomplete. In particular, the introduction of a new exponent characterising the finite-size correlation length allows one to extend hyperscaling beyond the upper critical dimension. Moreover, finite-size scaling is shown to be universal provided the correct scaling window is chosen. These recent developments also lead to the introduction of a new scaling relation analogous to one introduced by Fisher 50 years ago.

cond-mat.stat-mech↗

arXiv2024

The enigmatic exponent koppa and the story of finite-size scaling above the upper critical dimension

Scaling, hyperscaling and finite-size scaling were long considered problematic in theories of critical phenomena in high dimensions. The scaling relations themselves form a model-independent structure that any model-specific theory must adhere to, and they are accounted for by the simple principle of homogeneity. Finite-size scaling is similarly founded on the fundamental idea that only two length scales enter the game -- namely system length and correlation length. While all scaling relations are quite satisfactory for multitudes of physical systems in low dimensions, one fails in high dimensions...

cond-mat.stat-mech↗

arXiv2024

Critical and tricritical singularities from small-scale Monte Carlo simulations: The Blume-Capel model in two dimensions

We show that the study of critical properties of the Blume-Capel model at two dimensions can be deduced from Monte Carlo simulations with good accuracy even for small system sizes when one analyses the behaviour of the zeros of the partition function. The phase diagram of the model displays a line of second-order phase transitions ending at a tricritical point, then a line of first-order transitions. We concentrate on critical and tricritical properties and compare the accuracy achieved via standard finite-size scaling of thermodynamic quantities with that from the zeros analysis. This latter analysis showcases spectacular precision, even for systems as small as 64 spins! We also show that the zeros are very sensitive to subtle crossover effects.

cond-mat.stat-mech↗

arXiv2023

On a previously unpublished work with Ralph Kenna

This is part of an unpublished work in collaboration with Ralph Kenna. It was probably not mature enough at the time it was submitted more than ten years ago and it was rejected by the editors, but some of the ideas had later been published partially in subsequent works. I believe that this "draft" reveals a lot about Ralph's enthusiasm and audacity and deserves to be published now, maybe as a part of his legacy.

cond-mat.stat-mech↗

arXiv2023

The extraordinary story of Sinann -- the inspirational figure who gave her name to Ireland longest river -- and how she arose Ireland's resilient female icons

When local authorities recently selected a neoclassical male "river god head" of colonial origin to represent Ireland's longest river, it was welcomed as "harking back to Irish mythology". The council, local historians and townsfolk were unaware that in Irish mythology the figure associated with the river is a woman -- not a man. Her name is Sinann, and she had been written out of Ireland's national iconography after centuries of colonial destruction of Gaelic heritage. When mathematical investigation into Irish mythology brought Sinann's story to the people via local media, reaction was immediate. Street performances in support of Sinann were backed by letters in newspapers and a petition signed by hundreds of people demanding education about their heritage - and respect for women. How did this happen and what is the story behind Sinann, her diminution, and her rising? Here we recount how modern-day mathematics exposed the colonial imposter as stemming from the Ossianic controversy 250 years ago. We also discuss how a Victorian-era translation of her story from the original Irish turned what was an inspirational creation myth into a tale of a disobedient girl seeking knowledge to which she had no entitlement. This flawed narrative entered the public domain -- in encyclopaedias, on websites, and even in academic literature. Here we cast off colonial baggage to present a new, more accurate translation of Sinann's story alongside a new interpretation -- more amenable to a receptive public seeking enlightenment. Inspired by Sinann's rising, we also use artistic measures to invoke other Irish resilient female icons to rise up and take their rightful place in Irish iconography.

physics.soc-ph↗

arXiv2023

"The greatest Poet that has [n]ever existed" -- A Narrative Networks Analysis of the Poems of Ossian

Surprising as it may seem, applications of statistical methods to physics were inspired by the social sciences, which in turn are linked to the humanities. So perhaps it is not as unlikely as it might first appear for a group of statistical physicists and humanists to come together to investigate one of the subjects of Thomas Jefferson's poetic interests from a scientific point of view. And that is the nature of this article: a collaborative interdisciplinary analysis of the works of a figure Jefferson described as a ''rude bard of the North'' and ''the greatest Poet that has ever existed.'' In 2012, a subset of this team embraced an increase in interdisciplinary methods to apply the new science of complex networks to longstanding questions in comparative mythology. Investigations of network structures embedded in epic narratives allowed universal properties to be identified and ancient texts to be compared to each other. The approach inspired new challenges in mathematics, physics and even processes in industry, thereby illustrating how collaborations of this nature can be mutually beneficial and can capture the attention of a public, often ill-served by academic communication and dissemination. This article derives from these works, and from our consistent objective to help bridge the perceived gap between the natural sciences and the humanities. First we discuss the history of relationships between the two. Then we discuss the origins of the poems of Ossian and Jefferson's interests. We follow with our statistical approach in the next section. In the final section, we explore ideas for future research on these themes and discuss the potential of collaborative pursuits of human curiosity to overcome the two cultures dichotomy and embrace a scientific- and humanities-literate information age.

physics.soc-ph↗

arXiv2023

Exact coefficients of finite-size corrections in the Ising model with Brascamp-Kunz boundary conditions and their relationships for strip and cylindrical geometries

We derive exact finite-size corrections for the free energy $F$ of the Ising model on the ${\cal M} \times 2 {\cal N}$ square lattice with Brascamp-Kunz boundary conditions. We calculate ratios $r_p(\rho)$ of $p$th coefficients of F for the infinitely long cylinder (${\cal M} \to \infty$) and the infinitely long Brascamp-Kunz strip (${\cal N} \to \infty$) at varying values of the aspect ratio $\rho={(\cal M}+1) / 2{\cal N}$. Like previous studies have shown for the two-dimensional dimer model, the limiting values $p \to \infty$ of $r_p(\rho)$ exhibit abrupt anomalous behaviour at certain values of $\rho$. These critical values of $\rho$ and the limiting values of the finite-size-expansion-coefficient ratios differ, however, between the two models.

cond-mat.stat-mech↗

arXiv2023

Potts Model with Invisible States: A Review

The Potts model with invisible states was introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where $Z_q$ symmetry is spontaneously broken. It differs from the ordinary $q$-state Potts model in that each spin, besides the usual $q$ visible states, can be also in any of $r$ so-called invisible states. Spins in an invisible state do not interact with their neighbours but they do contribute to the entropy of the system. As a consequence, an increase in $r$ may cause a phase transition to change from second to first order. Potts models with invisible states describe a number of systems of interest in physics and beyond and have been treated by various tools of statistical and mathematical physics. In this paper we aim to give a review of this fundamental topic.

cond-mat.stat-mech↗

arXiv2022

Phase transitions above the upper critical dimension

These lecture notes provide an overview of the renormalization group (RG) as a successful framework to understand critical phenomena above the upper critical dimension $d_{\rm uc}$. After an introduction to the scaling picture of continuous phase transitions, we discuss the apparent failure of the Gaussian fixed point to capture scaling for Landau mean-field theory, which should hold in the thermodynamic limit above $d_{\rm uc}$. We recount how Fisher's dangerous-irrelevant-variable formalism applied to thermodynamic functions partially repairs the situation but at the expense of hyperscaling and finite-size scaling, both of which were, until recently, believed not to apply above $d_{\rm uc}$. We recall limitations of various attempts to match the RG with analytical and numerical results for Ising systems. We explain how the extension of dangerous irrelevancy to the correlation sector is key to marrying the above concepts into a comprehensive RG scaling picture that renders hyperscaling and finite-size scaling valid in all dimensions. We collect what we believe is the current status of the theory, including some new insights and results. This paper is in grateful memory of Michael Fisher who introduced many of the concepts discussed and who, half a century later, contributed to their advancement.

cond-mat.stat-mech↗

arXiv2022

Network analysis of the Kyiv bylyny cycle -- east Slavic epic narratives

In recent times, the advent of network science permitted new quantitative approaches to literary studies. Here we bring the Kyiv bylyny cycle into the field - East Slavic epic narratives originating in modern-day Ukraine. By comparing them to other prominent European epics, we identify universal and distinguishing properties of the social networks in bylyny. We analyse community structures and rank the most important characters. The method allows to bolster hypotheses from humanities literature - such as the position of Prince Volodymyr - and to generate new ones We show how the Kyiv cycle of bylyny fits very well with narrative networks from other nations - especially heroic ones. We anticipate that, besides delivering new narratological insights, this study will aid future scholars and interested public to navigate their way through Ukraine's epic story and identify its heroes.

physics.soc-ph↗

arXiv2022

Big fish and small ponds: why the departmental h-index should not be used to rank universities

The size-dependent nature of the so-called group or departmental h-index is reconsidered in this paper. While the influence of unit size on such collective measures was already demonstrated a decade ago, institutional ratings based on this metric can still be found and still impact on the reputations and funding of many research institutions. The aim of this paper is to demonstrate the fallacy of this approach to collective research-quality assessment in a simple way, focusing on the h-index in its original form. We show that randomly reshuffling real scientometric data (varying numbers of citations) amongst institutions of varying size, while maintaining the volume of their research outputs, has little effect on their departmental h-index. This suggests that the relative position in ratings based on the collective h-index is determined not only by quality (impact) of particular research outputs but by their volume. Therefore, the application of the collective h-index in its original form is disputable as a basement for comparison at aggregated levels such as to research groups, institutions or journals. We suggest a possible remedy for this failing which is implementable in a manner that is as simple and understandable as the h-index itself.

cs.DL↗

arXiv2021

Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws

We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of `+' or `$-$', `up' or `down', `yes' or `no'), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us to derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. We find the delicate interplay of the two power laws leads to new universality classes.

cond-mat.stat-mech↗

arXiv2021

Extracting partition function zeros from Fukui-Todo simulations

The Fukui-Todo algorithm is an important element of the array of simulational approaches to tackling critical phenomena in statistical physics. The partition-function-zero approach is of fundamental importance to understanding such phenomena and a precise tool to measure their properties. However, because the Fukui-Todo algorithm bypasses sample-by-sample energy computation, zeros cannot easily be harnessed through the energy distribution. Here this obstacle is overcome by a novel reweighting technique and zero-detection protocol. The efficacy of the approach is demonstrated in simple iconic models which feature transitions of both first and second order.

cond-mat.stat-mech↗

arXiv2020

Narrative structure of A Song of Ice and Fire creates a fictional world with realistic measures of social complexity

Network science and data analytics are used to quantify static and dynamic structures in George R.R. Martin's epic novels, A Song of Ice and Fire, works noted for their scale and complexity. By tracking the network of character interactions as the story unfolds, it is found that structural properties remain approximately stable and comparable to real-world social networks. Furthermore, the degrees of the most connected characters reflect a cognitive limit on the number of concurrent social connections that humans tend to maintain. We also analyse the distribution of time intervals between significant deaths measured with respect to the in-story timeline. These are consistent with power-law distributions commonly found in inter-event times for a range of non-violent human activities in the real world. We propose that structural features in the narrative that are reflected in our actual social world help readers to follow and to relate to the story, despite its sprawling extent. It is also found that the distribution of intervals between significant deaths in chapters is different to that for the in-story timeline; it is geometric rather than power law. Geometric distributions are memoryless in that the time since the last death does not inform as to the time to the next. This provides measurable support for the widely held view that significant deaths in A Song of Ice and Fire are unpredictable chapter-by-chapter.

physics.soc-ph↗

arXiv2020

Universality and exact finite-size corrections for spanning trees on cobweb and fan networks

Universality is a cornerstone of theories of critical phenomena. It is well understood in most systems especially in the thermodynamic limit. Finite-size systems present additional challenges. Even in low dimensions, universality of the edge and corner contributions to free energies and response functions is less well understood. The question arises of how universality is maintained in correction-to-scaling in systems of the same universality class but with very different corner geometries. 2D geometries deliver the simplest such examples that can be constructed with and without corners. To investigate how the presence and absence of corners manifest universality, we analyze the spanning tree generating function on two finite systems, namely the cobweb and fan networks. We address how universality can be delivered given that the finite-size cobweb has no corners while the fan has four. To answer, we appeal to the Ivashkevich-Izmailian-Hu approach which unifies the generating functions of distinct networks in terms of a single partition function with twisted boundary conditions. This unified approach shows that the contributions to the individual corner free energies of the fan network sum to zero so that it precisely matches that of the web. Correspondence in each case with results established by alternative means for both networks verifies the soundness of the algorithm. Its range of usefulness is demonstrated by its application to hitherto unsolved problems-namely the exact asymptotic expansions of the logarithms of the generating functions and the conformal partition functions for fan and cobweb geometries. Thus, the resolution of a universality puzzle demonstrates the power of the algorithm and opens up new applications in the future.

cond-mat.stat-mech↗

arXiv2020

Ising model with variable spin/agent strengths

We introduce varying spin strengths to the Ising model, a central pillar of statistical physics. With inhomogeneous physical systems in mind, but also anticipating interdisciplinary applications, we present the model on network structures of varying degrees of complexity. We solve it for the generic case of power-law spin strength and find that, with a self-averaging free energy, the model has a rich phase diagram with new universality classes. Indeed, the degree of complexity added by variable spins is on a par to that added by endowing simple networks with increasingly realistic geometries. It is suitable for modeling emergent phenomena in many-body systems in contexts where non-identicality of spins or agents plays an essential role and for exporting statistical physics concepts beyond physics.

cond-mat.stat-mech↗