arXiv subjects

Bertrand Berche

Publications and source records attributed to Bertrand Berche.

At least 19 recordsLinked to original sources

arXiv2026

Mean-field theory for quantum spin chains

Mean-field theory is a widely used approximation for describing phase transitions, particularly effective above the upper critical dimension. Its origins can be traced back to the van der Waals theory of the liquid-gas transition and Weiss's molecular field theory of the paramagnetic-ferromagnetic transition. However, it was Lev D. Landau who provided a unifying and general framework applicable to a broad class of physical systems. The mean-field approach typically involves neglecting thermal fluctuations, which is a reasonable assumption in many classical contexts. However, its application to quantum phase transitions at zero temperature is less common. The aim of this short pedagogical paper is to explore and clarify the use of the mean-field approach in the less familiar domain of quantum phase transitions. We specifically consider the Ising model and the Blume-Capel model.

cond-mat.stat-mech↗

arXiv2026

Horizon Microstructure Thermodynamics in AdS Black Holes: Smarr-Consistent Excitation Enthalpy

In this work we formulate a horizon-microstructure description of four-dimensional AdS black holes in which a horizon of area $A$ is resolved into $\mathcal{N}=A/a_p$ microscopic sites and $N$ occupied horizon sites. The central result is that the combinatorics of this partially occupied horizon sector yields the entropy directly: in the finite-filling regime the leading term is proportional to the area, and the maximal-entropy filling reproduces the Bekenstein--Hawking law with $a_p=4\ln 2\ \ell_{p}^{2}$. Subleading corrections include a subtractive logarithmic term and an inverse-area expansion. We then show that this partially occupied regime admits a thermodynamic justification from an extended first law with chemical potential $\mu$, a Smarr-consistent excitation enthalpy $\delta M(A,P,N)$, and an AdS control parameter $u=PS$. In this interpretation, the combinatorics provides the dominant horizon entropy, while the thermodynamic sector supplies a dressing that selects the equilibrium filling and assigns a finite excitation cost to departures from a reference partially occupied configuration.

hep-th↗

arXiv2026

Orbital Angular Momentum Textures and Currents in a Discrete Helix: Equilibrium and Linear Response

Recently, nonequilibrium orbital angular momentum in low-dimensional systems has attracted renewed attention. Here we introduce a minimal three-orbital tight-binding model for a single helical chain and show that chirality alone generates a momentum-dependent orbital-angular-momentum texture through Slater--Koster hybridization in the local basis $(p_r,p_\phi,p_z)$, without requiring atomic spin--orbit coupling. In the single-helix geometry, the radial orbital texture vanishes identically, while the azimuthal and longitudinal components remain finite and arise from the odd-in-momentum $(p_z,p_r)$ and $(p_r,p_\phi)$ sectors. As a result, the equilibrium average orbital texture vanishes by parity, although persistent-like orbital angular momentum currents may still exist and imply chirality-dependent end magnetization in a finite helix. Under an applied longitudinal electric field, the system develops a finite orbital Edelstein response, whereas the projected longitudinal orbital-current conductivity vanishes in the linear regime by parity. When spin degrees of freedom are included, the orbital texture acts as a source of spin polarization through orbital-to-spin transduction. The resulting spin response is controlled by orbital overlap scales much larger than the bare relativistic spin--orbit scale, making it a stronger candidate for spin injection than the conventional spin Edelstein mechanism. These results identify chirality as the minimal microscopic ingredient for generating orbital angular momentum response in one-dimensional systems and support an orbital route to spin selectivity in chiral conductors.

cond-mat.mes-hall↗

arXiv2025

Phase transition properties via partition function zeros: The Blume-Capel ferromagnet revisited

Since the landmark work of Lee and Yang, locating the zeros of the partition function in the complex magnetic-field plane has become a powerful method for studying phase transitions. Fisher later extended this approach to complex temperatures, and subsequent generalizations introduced other control parameters, such as the crystal field. In previous works [Moueddene et al, J. Stat. Mech. (2024) 023206; Phys. Rev. E 110, 064144 (2024)] we applied this framework to the two- and three-dimensional Blume-Capel model -- a system with a rich phase structure where a second-order critical line meets a first-order line at a tricritical point. We showed that the scaling of Lee-Yang, Fisher, and crystal-field zeros yields accurate critical exponents even for modest lattice sizes. In the present study, we extend this analysis and demonstrate that simulations need not be performed exactly at the nominal transition point to obtain reliable exponent estimates. Strikingly, small system sizes are sufficient, which not only improves methodological efficiency but also advances the broader goal of reducing the carbon footprint of large-scale computational studies.

cond-mat.stat-mech↗

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

Critical and tricritical behavior of the $d=3$ Blume-Capel model: Results from small-scale Monte Carlo simulations

We investigate the location of the critical and tricritical points of the three-dimensional Blume-Capel model by analyzing the behavior of the first Lee-Yang zero, the density of partition function zeros, and higher-order cumulants of the magnetization. Our analysis is conducted through Monte Carlo simulations, intentionally using only small system sizes. We demonstrate that this approach yields excellent results for studying the critical behavior of the model. Our findings indicate that at the tricritical point, where logarithmic corrections are anticipated, the numerical results align closely with the theoretical exponents describing these corrections. These expected values are then employed to accurately determine the coordinates of the tricritical point. At the model's critical point, the corrections correspond to those of the three-dimensional Ising model criticality, which we also use to precisely ascertain the critical temperature at zero crystal field. Additionally, we utilize more traditional thermodynamic quantities to validate the self-consistency of our analysis.

cond-mat.stat-mech↗

arXiv2024

Minimal Model for Chirally Induced Spin Selectivity: Chirality, Spin-orbit coupling, Decoherence and Tunneling

Here we review a universal model for chirally induced spin-selectivity (CISS) as a standalone effect occurring in chiral molecules. We tie together the results of forward scattering in the gas phase to the results for photoelectrons in chiral self-assembled monolayers and the more contemporary results in two terminal transport setups. We discuss the ingredients that are necessarily present in all experiments to date, which we identify as: i) chirality, be it point, helical or configurational, ii) the spin-orbit coupling as the spin active coupling of atomic origin, iii) decoherence as a time-reversal symmetry breaking mechanism that avoids reciprocity relations in the linear regime and finally iv) tunneling that accounts for the magnitude of the spin polarization effect. This proposal does not discard other mechanisms that can yield comparable spin effects related to interactions of the molecule to contacts or substrates that have been proposed but that are less universal or apply to particular situations. Finally, we discuss recent results suggesting CISS as a molecular phenomenon in the real of enantiomer selectivity, coherent electron transfer, and spin effects in chiroptical activity.

cond-mat.mes-hall↗

arXiv2024

Differential geometry, a possible avenue for thermal ablation in oncology?

We report a model for hyperthermia therapies based on heat diffusion in a biological tissue containing a topological defect. Biological tissues behave like active liquid crystals with the presence of topological defects which are likely to anchor tumors during the metastatic phase of cancer evolution and the therapy challenge is to destroy the cancer cells without damaging surrounding healthy tissues. The defect creates an effective non-Euclidean geometry for low-energy excitations, modifying the bio-heat equation. Applications to protocols of thermal ablation for various biological tissues (liver, prostate, and skin) is analyzed and discussed.

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

The advance of Mercury's perihelion

A very famous ``test'' of the General Theory of Relativity (GTR) is the advance of Mercury's perihelion (and of other planets too). To be more precise, this is not a prediction of General Relativity, since the anomaly was known in the XIXth century, but no consistent explanation had been found yet at the time GTR was elaborated. Einstein came up with a solution to the problem in 1914. In the case of Mercury, the closest planet to the Sun, the effect is more pronounced than for other planets, and observed from Earth; there is an advance of the perihelion of Mercury of about 5550~arc seconds per century (as/cy). Among these, about $5000$ are due to the equinox precession (the precise value is {$5025.645$}~as/cy) and about $500$ ({$531.54$}) to the influence of the external planets. The remaining, about $50$~as/cy ({$42.56$}), are not understood within Newtonian mechanics. Here, we revisit the problem in some detail for a presentation at the undergraduate level.

gr-qc↗

arXiv2024

Ralph Kenna's scaling relations in critical phenomena

In this note, we revisit the scaling relations among ``hatted critical exponents'' which were first derived by Ralph Kenna, Des Johnston and Wolfhard Janke, and we propose an alternative derivation for some of them. For the scaling relation involving the behavior of the correlation function, we will propose an alternative form since we believe that the expression is erroneous in the work of Ralph and his collaborators.

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↗

arXiv2024

Minimal Model for Chirally Induced Spin Selectivity: Spin-orbit coupling, tunneling and decoherence

Chirally Induced Spin Selectivity (CISS) is a transport phenomenon observed in both linear and non-linear regimes, where the spin-orbit coupling (SOC) acts as the key driver and electron tunneling serves as the dominant mechanism for charge transfer. Despite SOC's inherent time-reversal symmetry (TRS) preservation, conventional reciprocity relations limit spin polarization and the differential treatment of spin species. In experimental systems, an additional factor, spin-independent decoherence, disrupts TRS and reciprocity. We introduce decoherence using the Buttiker voltage probe within the scattering matrix framework. Our results reveal the importance of under-the-barrier decoherence as an order-of-magnitude polarization enhancement mechanism. Polarization arises by the disruption of spin precession around the spin-orbit magnetic field with a new spin component along the field direction. The alignment of polarization depends on interference effects produced by the voltage probe. We discuss the connection of our model to a more realistic decoherence mechanism in molecular systems.

cond-mat.mes-hall↗

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

On the possibility of classical vacuum polarization and magnetization

It is common practice to take for granted the equality (up to the constant $\varepsilon_0$) of the electric displacement ($\bf{D}$) and electric ($\bf{E}$) field vectors in vacuum. The same happens with the magnetic field ($\bf{H}$) and the magnetic flux density ($\bf{B}$) vectors (up to the constant $\mu_0^{-1}$). The fact that gravity may change this by effectively inducing dielectric or magnetic responses to the primary fields is commonly overlooked. It is the purpose of this communication to call attention to classical polarization or magnetization of the vacuum due to the concomitant presence of gravitational and electromagnetic sources. The formalism of differential forms (exterior calculus) is used since it provides a clear-cut way to achieve this. This work offers new routes for possible detection of various spacetime geometries via their electromagnetic manifestations and the way they influence light propagation.

gr-qc↗

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↗

arXiv2023

Geometric theory of topological defects: methodological developments and new trends

Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the art of the differential geometry of nematic liquid crystals, with a special emphasis on linear defects. We then discuss unexpected but deep connections with cosmology and high-energy-physics, and conclude with a review on defect engineering for transport phenomena.

cond-mat.soft↗