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Bertrand Berche

Publications and source records attributed to Bertrand Berche.

At least 91 records · Page 5Linked to original sources
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↗
arXiv2009

Comment on "Equilibrum spin currents: Non-Abelian Gauge Invariance and Color Diamagnetism in Condensed Matter"

In a recent paper [Phys. Rev. Lett. 101, 106601], I. V. Tokatly addresses a non Abelian formulation of spin orbit interaction in condensed matter, restricting to a gauge symmetric scenario. In this comment we draw attention on the relevance of gauge symmetry breaking on such formulation and point out why this is a necessary ingredient for properly describing the associated diamagnetic color currents.

cond-mat.mes-hall↗
arXiv2008

Extended Scaling in High Dimensions

We apply and test the recently proposed "extended scaling" scheme in an analysis of the magnetic susceptibility of Ising systems above the upper critical dimension. The data are obtained by Monte Carlo simulations using both the conventional Wolff cluster algorithm and the Prokof'ev-Svistunov worm algorithm. As already observed for other models, extended scaling is shown to extend the high-temperature critical scaling regime over a range of temperatures much wider than that achieved conventionally. It allows for an accurate determination of leading and sub-leading scaling indices, critical temperatures and amplitudes of the confluent corrections.

cond-mat.stat-mech↗
arXiv2008

Universal ratios of critical amplitudes in the Potts model universality class

Monte Carlo (MC) simulations and series expansions (SE) data for the energy, specific heat, magnetization, and susceptibility of the three-state and four-state Potts model and Baxter-Wu model on the square lattice are analyzed in the vicinity of the critical point in order to estimate universal combinations of critical amplitudes. We also form effective ratios of the observables close to the critical point and analyze how they approach the universal critical-amplitude ratios. In particular, using the duality relation, we show analytically that for the Potts model with a number of states $q\le 4$, the effective ratio of the energy critical amplitudes always approaches unity linearly with respect to the reduced temperature. This fact leads to the prediction of relations among the amplitudes of correction-to-scaling terms of the specific heat in the low- and high-temperature phases. It is a common belief that the four-state Potts and the Baxter-Wu model belong to the same universality class. At the same time, the critical behavior of the four-state Potts model is modified by logarithmic corrections while that of the Baxter-Wu model is not. Numerical analysis shows that critical amplitude ratios are very close for both models and, therefore, gives support to the hypothesis that the critical behavior of both systems is described by the same renormalization group fixed point.

cond-mat.stat-mech↗
arXiv2008

Numerical revision of the universal amplitude ratios for the two-dimensional 4-state Potts model

Monte Carlo (MC) simulations and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the ferromagnetic 4-state Potts model on the square lattice are analyzed in a vicinity of the critical point in order to estimate universal combinations of critical amplitudes. The quality of the fits is improved using predictions of the renormalization group (RG) approach and of conformal invariance, and restricting the data within an appropriate temperature window. The RG predictions on the cancelation of the logarithmic corrections in the universal amplitude ratios are tested. A direct calculation of the effective ratio of the energy amplitudes using duality relations explicitly demonstrates this cancelation of logarithms, thus supporting the predictions of RG. We emphasize the role of corrections of background terms on the determination of the amplitudes. The ratios of the critical amplitudes of the susceptibilities obtained in our analysis differ significantly from those predicted theoretically and supported by earlier SE and MC analysis. This disagreement might signal that the two-kink approximation used in the analytical estimates is not sufficient to describe with fair accuracy the amplitudes of the 4-state model.

cond-mat.stat-mech↗
arXiv2008

Gauge symmetry breaking and topological quantization for the Pauli Hamiltonian

We discuss the Pauli Hamiltonian within a ${SU(2)}$ gauge theory interpretation, where the gauge symmetry is broken. This interpretation carries directly over to the structural inversion asymmetric spin-orbit interactions in semiconductors and offers new insight into the problem of spin currents in the condensed matter environment. The central results is that symmetry breaking leads to zero spin conductivity in contrast to predictions of Gauge symmetric treatments. Computing the translation operator commutation relations comprising the simplest possible structural inversion asymmetry due to an external electric field, we derive a new condition for orbit quantization. The relation between the topological nature of this effect is consistent with our non-Abelian gauge symmetry breaking scenario.

cond-mat.mes-hall↗
arXiv2008

Interplay of topological and structural defects in the 2D XY model

The present work is devoted to the investigation of the interaction between vortices (topological defects) and site-impurities (structural defects) in the 2D XY model and its influence on the well-known properties of the pure system. The main goal is a theoretical description of the Berezinskii-Kosterlitz-Thouless (BKT) temperature reduction by quenched non-magnetic impurities, based on the vacancy-vortex interactions and the vortex-pair dissociation mechanism of the transition. The non-magnetic impurity interaction with a system of vortices can be found either from the phenomenological theory of topological defects or from the Villain model. We take both paths and compare the results obtained. Our prediction for the BKT temperature reduction is confirmed by the available Monte Carlo data.

cond-mat.stat-mech↗
arXiv2007

A study of logarithmic corrections and universal amplitude ratios in the two-dimensional 4-state Potts model

Monte Carlo (MC) and series expansion (SE) data for the energy, specific heat, magnetization and susceptibility of the two-dimensional 4-state Potts model in the vicinity of the critical point are analysed. The role of logarithmic corrections is discussed and an approach is proposed in order to account numerically for these corrections in the determination of critical amplitudes. Accurate estimates of universal amplitude ratios $A_+/A_-$, $Γ_+/Γ_-$, $Γ_T/Γ_-$ and $R_C^\pm$ are given, which arouse new questions with respect to previous works.

cond-mat.stat-mech↗
arXiv2007

Logarithmic corrections and universal amplitude ratios in the 4-state Potts model

Monte Carlo and series expansion data for the energy, specific heat, magnetisation and susceptibility of the 4-state Potts model in the vicinity of the critical point are analysed. The role of logarithmic corrections is discussed. Estimates of universal ratios A_+/A_-, $Γ_+/Γ_L$, $Γ_T/Γ_L$ and R_c^+ are given.

cond-mat.stat-mech↗
arXiv2006

The 2D XY model on a finite lattice with structural disorder: quasi-long-range ordering under realistic conditions

We present an analytic approach to study concurrent influence of quenched non-magnetic site-dilution and finiteness of the lattice on the 2D XY model. Two significant deeply connected features of this spin model are: a special type of ordering (quasi-long-range order) below a certain temperature and a size-dependent mean value of magnetisation in the low-temperature phase that goes to zero (according to the Mermin-Wagner-Hohenberg theorem) in the thermodynamic limit. We focus our attention on the asymptotic behaviour of the spin-spin correlation function and the probability distribution of magnetisation. The analytic approach is based on the spin-wave approximation valid for the low-temperature regime and an expansion in the parameters which characterise the deviation from completely homogeneous configuration of impurities. We further support the analytic considerations by Monte Carlo simulations performed for different concentrations of impurities and compare analytic and MC results. We present as the main quantitative result of the work the exponent of the spin-spin correlation function power law decay. It is non universal depending not only on temperature as in the pure model but also on concentration of magnetic sites. This exponent characterises also the vanishing of magnetisation with increasing lattice size.

cond-mat.stat-mech↗
arXiv2006

Perturbation expansion for the diluted two-dimensional XY model

We study the quasi-long-range ordered phase of a 2D XY model with quenched site-dilution using the spin-wave approximation and expansion in the parameter which characterizes the deviation from completely homogeneous dilution. The results, obtained by keeping the terms up to the third order in the expansion, show good accordance with Monte Carlo data in a wide range of dilution concentrations far enough from the percolation threshold. We discuss different types of expansion.

cond-mat.stat-mech↗
arXiv2006

Quasi-long-range ordering in a finite-size 2D Heisenberg model

We analyse the low-temperature behaviour of the Heisenberg model on a two-dimensional lattice of finite size. Presence of a residual magnetisation in a finite-size system enables us to use the spin wave approximation, which is known to give reliable results for the XY model at low temperatures T. For the system considered, we find that the spin-spin correlation function decays as 1/r^eta(T) for large separations r bringing about presence of a quasi-long-range ordering. We give analytic estimates for the exponent eta(T) in different regimes and support our findings by Monte Carlo simulations of the model on lattices of different sizes at different temperatures.

hep-th↗
arXiv2005

Nematic phase transitions in two-dimensional systems

Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P\_4$. The system is studied through standard Finite-Size Scaling and conformal rescaling of density profiles or correlation functions. The low temperature limit is discussed in the spin wave approximation and confirms the numerical results, while the value of the correlation function exponent at the deconfining transition seems controversial.

cond-mat.stat-mech↗
arXiv2005

Introduction to thermodynamics of spin models in the Hamiltonian limit

A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian, and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices.

physics.ed-ph↗
arXiv2005

Topological transition in a two-dimensional model of liquid crystal

Simulations of nematic-isotropic transition of liquid crystals in two dimensions are performed using an O(2) vector model characterised by non linear nearest neighbour spin interaction governed by the fourth Legendre polynomial $P\_4$. The system is studied through standard Finite-Size Scaling and conformal rescaling of density profiles of correlation functions. A topological transition between a paramagnetic phase at high temperature and a critical phase at low temperature is observed. The low temperature limit is discussed in the spin wave approximation and confirms the numerical results.

cond-mat.stat-mech↗
arXiv2005

Monte Carlo Study of Phase Transitions in the Bond-Diluted 3D 4-State Potts Model

Large-scale Monte Carlo simulations of the bond-diluted three-dimensional 4-state Potts model are performed. The phase diagram and the physical properties at the phase transitions are studied using finite-size scaling techniques. Evidences are given for the existence of a tricritical point dividing the phase diagram into a regime where the transitions remain of first order and a second regime where the transitions are softened to continuous ones by the influence of disorder. In the former regime, the nature of the transition is essentially clarified through an analysis of the energy probability distribution. In the latter regime critical exponents are estimated. Rare and typical events are identified and their role is qualitatively discussed in both regimes.

cond-mat.stat-mech↗
arXiv2004

Random Ising model in three dimensions: theory, experiment and simulation - a difficult coexistence

We discuss different approaches for studying the influence of disorder in the three-dimensional Ising model. From the theoretical point of view, renormalisation group calculations provide quite accurate results. Experiments carried out on crystalline mixtures of compounds lead to measurements as accurate as three digits on the values of critical exponents. Numerically, extensive Monte Carlo simulations then pretend to be of comparable accuracy. Life becomes complicated when details are compared between the three approaches.

cond-mat.stat-mech↗