arXiv subjects

B. Berche

Publications and source records attributed to B. Berche.

At least 19 recordsLinked to original sources

arXiv2023

When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension

We progress finite-size scaling in systems with free boundary conditions above their upper critical dimension, where in the thermodynamic limit critical scaling is described by mean-field theory. Recent works show that the correlation length is not bound by the system's physical size, a belief that long held sway. Instead, two scaling regimes can be observed - at the critical and pseudo-critical temperatures. We demonstrate that both are manifest for free boundaries. We use numerical simulations of the $d=5$ Ising model to analyse the magnetization, susceptibility, magnetization Fourier modes and the partition function zeros. While some of the response functions hide the dual finite-size scaling, the precision enabled by the analysis of Lee-Yang zeros allows this be brought to the fore. In particular, finite-size scaling of leading zeros at the pseudo-critical point confirms recent predictions coming from correlations exceeding the system size. This paper is dedicated to Jaroslav Ilnytskyi on the occasion of his 60th birthday.

cond-mat.stat-mech↗

arXiv2023

The fifty-year quest for universality in percolation theory in high dimensions

Although well described by mean-field theory in the thermodynamic limit, scaling has long been puzzling for finite systems in high dimensions. This raised questions about the efficacy of the renormalization group and foundational concepts such as universality, finite-size scaling and hyperscaling, until recently believed not to be applicable above the upper critical dimension. Significant theoretical progress has been made resolving these issues, and tested in numerous simulational studies of spin models. This progress rests upon superlinearity of correlation length, a notion that for a long time encountered resistance but is now broadly accepted. Percolation theory brings added complications such as proliferation of interpenetrating clusters in apparent conflict with suggestions coming from random-graph asymptotics and a dearth of reliable simulational guidance. Here we report on recent theoretical progress in percolation theory in the renormalization group framework in high dimensions that accommodates superlinear correlation and renders most of the above concepts mutually compatible under different boundary conditions. Results from numerical simulations for free and periodic boundary conditions which differentiate between previously competing theories are also presented. Although still fragmentary, these Monte Carlo results support the new framework which restores the renormalization group and foundational concepts on which it rests.

cond-mat.stat-mech↗

arXiv2023

Spin polarization induced by decoherence in a tunneling one-dimensional Rashba model

Basic questions on the nature of spin polarization in two terminal systems and the way in which decoherence breaks Time-Reversal Symmetry (TRS) are analyzed. We exactly solve several one-dimensional models of tunneling electrons and show the interplay of spin precession and decay of the wavefunction in either a U(1) magnetic field or an effective Spin-Orbit (SO) magnetic field. Spin polarization is clearly identified as the emergence of a spin component parallel to either magnetic field. We show that Onsager's reciprocity is fulfilled when time reversal symmetry is present and no spin polarization arises, no matter the barrier parameters or the SO strength. Introducing a Buttiker's decoherence probe, that preserves unitarity of time evolution, we show that breaking of TRS results in a strong spin polarization for realistic SO, and barrier strengths. We discuss the significance of these results as a very general scenario for the onset of the Chiral-Induced Spin Selectivity effect (CISS), now possibly matching experiments in a quantitative manner.

cond-mat.mes-hall↗

arXiv2020

On the energy of topological defect lattices

Since the logarithm function is the solution of Poisson's equation in two dimensions, it appears as the Coulomb interaction in two dimensions, the interaction between Abrikosov flux lines in a type II superconductor, or between line defects in elastic media, and so on. Lattices of lines interacting logarithmically are, therefore, a subject of intense research due to their manifold applications. The solution of the Poisson equation for such lattices is known in the form of an infinite sum since the late 1990's. In this article we present an alternative analytical solution, in closed form, in terms of the Jacobi theta function.

cond-mat.mes-hall↗

arXiv2019

Intrinsic Rashba coupling due to Hydrogen bonding in DNA

We present an analytical model for the role of hydrogen bonding on the spin-orbit coupling of model DNA molecule. Here we analyze in detail the electric fields due to the polarization of the Hydrogen bond on the DNA base pairs and derive, within tight binding analytical band folding approach, an intrinsic Rashba coupling which should dictate the order of the spin active effects in the Chiral-Induced Spin Selectivity (CISS) effect. The coupling found is ten times larger than the intrinsic coupling estimated previously and points to the predominant role of hydrogen bonding in addition to chirality in the case of biological molecules. We expect similar dominant effects in oligopeptides, where the chiral structure is supported by hydrogen-bonding and bears on orbital carrying transport electrons.

cond-mat.mes-hall↗

arXiv2017

Rashba spin-orbit interaction enhanced by graphene in-plane deformations

Graphene consists in a single-layer carbon crystal where 2$p_z$ electrons display a linear dispersion relation in the vicinity of the Fermi level, conveniently described by a massless Dirac equation in $2+1$ spacetime. Spin-orbit effects open a gap in the band structure and offer perspectives for the manipulation of the conducting electrons spin. Ways to manipulate spin-orbit couplings in graphene have been generally assessed by proximity effects to metals that do not compromise the mobility of the unperturbed system and are likely to induce strain in the graphene layer. In this work we explore the $\rm{U(1)}\times SU(2)$ gauge fields that result from the uniform stretching of a graphene sheet under a perpendicular electric field. Considering such deformations is particularly relevant due to the counter-intuitive enhancement of the Rashba coupling between 30-50% for small bond deformations well known from tight-binding and DFT calculations. We report the accessible changes that can be operated in the band structure in the vicinity of the K points as a function of the deformation strength and direction.

cond-mat.mes-hall↗

arXiv2017

A scientists' view of scientometrics: Not everything that counts can be counted

Like it or not, attempts to evaluate and monitor the quality of academic research have become increasingly prevalent worldwide. Performance reviews range from at the level of individuals, through research groups and departments, to entire universities. Many of these are informed by, or functions of, simple scientometric indicators and the results of such exercises impact onto careers, funding and prestige. However, there is sometimes a failure to appreciate that scientometrics are, at best, very blunt instruments and their incorrect usage can be misleading. Rather than accepting the rise and fall of individuals and institutions on the basis of such imprecise measures, calls have been made for indicators be regularly scrutinised and for improvements to the evidence base in this area. It is thus incumbent upon the scientific community, especially the physics, complexity-science and scientometrics communities, to scrutinise metric indicators. Here, we review recent attempts to do this and show that some metrics in widespread use cannot be used as reliable indicators research quality.

physics.soc-ph↗

arXiv2015

On the discontinuity of the specific heat of the Ising model on a scale-free network

We consider the Ising model on an annealed scale-free network with node-degree distribution characterized by a power-law decay $P(K)\sim K^{-λ}$. It is well established that the model is characterized by classical mean-field exponents for $λ>5$. In this note we show that the specific-heat discontinuity $δc_h$ at the critical point remains $λ$-dependent even for $λ>5$: $δc_h=3(λ-5)(λ-1)/[2(λ-3)^2]$ and attains its mean-field value $δc_h=3/2$ only in the limit $λ\to \infty$. We compare this behaviour with recent measurements of the $d$ dependency of $δc_h$ made for the Ising model on lattices with $d>4$ [Lundow P.H., Markström K., Nucl. Phys. B, 2015, Vol. 895, 305].

cond-mat.stat-mech↗

arXiv2015

Marginal dimensions of the Potts model with invisible states

We reconsider the mean-field Potts model with $q$ interacting and $r$ non-interacting (invisible) states. The model was recently introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where the $Z_q$-symmetry is spontaneously broken. We analyse the marginal dimensions of the model, i.e., the value of $r$ at which the order of the phase transition changes. In the $q=2$ case, we determine that value to be $r_c = 3.65(5)$; there is a second-order phase transition there when $r r_c$. We also analyse the region $1 \leq q<2$ and show that the change from second to first order there is manifest through a new mechanism involving {\emph{two}} marginal values of $r$. The $q=1$ limit gives bond percolation and some intermediary values also have known physical realisations. Above the lower value $r_{c1}$, the order parameters exhibit discontinuities at temperature $\tilde{t}$ below a critical value $t_c$. But, provided $r>r_{c1}$ is small enough, this discontinuity does not appear at the phase transition, which is continuous and takes place at $t_c$. The larger value $r_{c2}$ marks the point at which the phase transition at $t_c$ changes from second to first order. Thus, for $r_{c1}< r < r_{c2}$, the transition at $t_c$ remains second order while the order parameter has a discontinuity at $\tilde{t}$. As $r$ increases further, $\tilde{t}$ increases, bringing the discontinuity closer to $t_c$. Finally, when $r$ exceeds $r_{c2}$ $\tilde{t}$ coincides with $t_c$ and the phase transition becomes first order. This new mechanism indicates how the discontinuity characteristic of first order phase transitions emerges.

cond-mat.stat-mech↗

arXiv2015

On the role of Fourier modes in finite-size scaling above the upper critical dimension

Renormalization-group theory stands, since over 40 years, as one of the pillars of modern physics. As such, there should be no remaining doubt regarding its validity. However, finite-size scaling, which derives from it, has long been poorly understood above the upper critical dimension $d_c$ in models with free boundary conditions. Besides its fundamental significance for scaling theories, the issue is important at a practical level because finite-size, statistical-physics systems, with free boundaries above $d_c$, are experimentally accessible with long-range interactions. Here we address the roles played by Fourier modes for such systems and show that the current phenomenological picture is not supported for all thermodynamic observables either with free or periodic boundaries. Instead, the correct picture emerges from a sector of the renormalization group hitherto considered unphysical.

cond-mat.stat-mech↗

arXiv2015

Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks

We analyze the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as $P(k)\sim k^{-λ}$. We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee-Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case $λ> 5$, reproduces the zeros for the Ising model on a complete graph. For $3<λ< 5$ we derive the $λ$-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the $λ$-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when $3<λ<5$. Whereas in the former case the zeros are purely imaginary, they have a non zero real part in latter case, so that the celebrated Lee-Yang circle theorem is violated.

cond-mat.stat-mech↗

arXiv2015

Violation of Lee-Yang circle theorem for Ising phase transitions on complex networks

The Ising model on annealed complex networks with degree distribution decaying algebraically as $p(K)\sim K^{-λ}$ has a second-order phase transition at finite temperature if $λ> 3$. In the absence of space dimensionality, $λ$ controls the transition strength; mean-field theory applies for $λ>5$ but critical exponents are $λ$-dependent if $λ< 5$. Here we show that, as for regular lattices, the celebrated Lee-Yang circle theorem is obeyed for the former case. However, unlike on regular lattices where it is independent of dimensionality, the circle theorem fails on complex networks when $λ< 5$. We discuss the importance of this result for both theory and experiments on phase transitions and critical phenomena. We also investigate the finite-size scaling of Lee-Yang zeros in both regimes as well as the multiplicative logarithmic corrections which occur at $λ=5$.

cond-mat.stat-mech↗

arXiv2015

Finite-size scaling above the upper critical dimension in Ising models with long-range interactions

The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size scaling and hyperscaling take conventional forms. Above the upper critical dimension these forms break down and a new scaling scenario appears. Here we investigate this scaling behaviour in one-dimensional Ising ferromagnets with long-range interactions. We show that the correlation length scales as a non-trivial power of the linear system size and investigate the scaling forms. For interactions of sufficiently long range, the disparity between the correlation length and the system length can be made arbitrarily large, while maintaining the new scaling scenarios. We also investigate the behavior of the correlation function above the upper critical dimension and the modifications imposed by the new scaling scenario onto the associated Fisher relation.

cond-mat.stat-mech↗

arXiv2015

Predicting Results of the Research Excellence Framework using Departmental h-Index -- Revisited

We revisit our recent study [Predicting results of the Research Excellence Framework using departmental h-index, Scientometrics, 2014, 1-16; arXiv:1411.1996] in which we attempted to predict outcomes of the UK's Research Excellence Framework (REF~2014) using the so-called departmental $h$-index. Here we report that our predictions failed to anticipate with any accuracy either overall REF outcomes or movements of individual institutions in the rankings relative to their positions in the previous Research Assessment Exercise (RAE~2008).

cs.DL↗

arXiv2014

Fisher's scaling relation above the upper critical dimension

Fisher's fluctuation-response relation is one of four famous scaling formulae and is consistent with a vanishing correlation-function anomalous dimension above the upper critical dimension d_c. However, it has long been known that numerical simulations deliver a negative value for the anomalous dimension there. Here, the apparent discrepancy is attributed to a distinction between the system-length and correlation- or characteristic-length scales. On the latter scale, the anomalous dimension indeed vanishes above d_c and Fisher's relation holds in its standard form. However, on the scale of the system length, the anomalous dimension is negative and Fisher's relation requires modification. Similar investigations at the upper critical dimension, where dangerous irrelevant variables become marginal, lead to an analogous pair of Fisher relations for logarithmic-correction exponents. Implications of a similar distinction between length scales in percolation theory above d_c and for the Ginzburg criterion are briefly discussed.

cond-mat.stat-mech↗

arXiv2014

Equilibrium currents in a Corbino graphene ring

We address the description of a graphene Corbino disk in the context of a tight binding approach that includes both kinetic and Rashba spin-orbit coupling due to an external out-of-plane electric field. Persistent equilibrium currents are induced by an external magnetic field breaking time reversal symmetry. By direct diagonalization, we compute the spectrum and focus on the dispersion near the $K$ points at the Fermi level. The dispersion keenly reproduces that of a continuum model in spite of the complexity of the boundary conditions. We validate the assumptions of the continuum model in terms of predominant zig-zag boundaries conditions and weak sub-band coupling. The wave functions displaying the lowest transverse modes are obtained, showing the predominance of edge states with charge density at the zig-zag edges. The persistent charge currents, nevertheless, do not follow the traditional argument of current cancellation from levels below the Fermi level, and thus they depart in the tight-binding from those found in the continuum model.

cond-mat.mes-hall↗

arXiv2014

A new critical exponent koppa and its logarithmic counterpart koppa-hat

It is well known that standard hyperscaling breaks down above the upper critical dimension d_c, where the critical exponents take on their Landau values. Here we show that this is because, in standard formulations in the thermodynamic limit, distance is measured on the correlation-length scale. However, the correlation-length scale and the underlying length scale of the system are not the same at or above the upper critical dimension. Above d_c they are related algebraically through a new critical exponent koppa, while at d_c they differ through logarithmic corrections governed by an exponent koppa-hat. Taking proper account of these different length scales allows one to extend hyperscaling to all dimensions.

cond-mat.stat-mech↗

arXiv2013

Phase transitions in the Potts model on complex networks

The Potts model is one of the most popular spin models of statistical physics. The prevailing majority of work done so far corresponds to the lattice version of the model. However, many natural or man-made systems are much better described by the topology of a network. We consider the q-state Potts model on an uncorrelated scale-free network for which the node-degree distribution manifests a power-law decay governed by the exponent λ. We work within the mean-field approximation, since for systems on random uncorrelated scale-free networks this method is known to often give asymptotically exact results. Depending on particular values of q and λone observes either a first-order or a second-order phase transition or the system is ordered at any finite temperature. In a case study, we consider the limit q=1 (percolation) and find a correspondence between the magnetic exponents and those describing percolation on a scale-free network. Interestingly, logarithmic corrections to scaling appear at λ=4 in this case.

cond-mat.stat-mech↗