arXiv subjects

Jean-Yves Fortin

Publications and source records attributed to Jean-Yves Fortin.

At least 37 records · Page 2Linked to original sources

arXiv2013

Onsager phase factor of quantum oscillations in the organic metal theta-(BEDT-TTF)4CoBr4(C6H4Cl2)

De Haas-van Alphen oscillations are studied for Fermi surfaces illustrating the Pippard's model, commonly observed in multiband organic metals. Field- and temperature-dependent amplitude of the various Fourier components, linked to frequency combinations arising from magnetic breakdown between different bands, are considered. Emphasis is put on the Onsager phase factor of these components. It is demonstrated that, in addition to the usual Maslov index, field-dependent phase factors must be considered to precisely account for the data at high magnetic field. We present compelling evidence of the existence of such contributions for the organic metal theta-(BEDT-TTF)4CoBr4(C6H4Cl2).

cond-mat.str-el↗

arXiv2012

Nature of the global fluctuations in the spherical model at criticality

We study the universal nature of global fluctuations in the critical regime of the spherical model by evaluating the exact distribution of the magnetization and its absolute value in the thermodynamical limit, in the presence of a conjugate field. We show that the probability distribution function for this model is described by non-Gaussian asymptotics and non-symmetric characteristics which depend on the dimension of the system 2<d<4. Relation with extreme statistics of independent wavelength modes is discussed.

cond-mat.stat-mech↗

arXiv2012

Organic conductors in high magnetic fields: model systems for quantum oscillations physics

Even though organic conductors have complicated crystalline structure with low symmetry and large unit cell, band structure calculations predict multiband quasi-two dimensional electronic structure yielding very simple Fermi surface in most cases. Although few puzzling experimental results are observed, data of numerous compounds are in agreement with calculations which make them suitable systems for studying magnetic quantum oscillations in networks of orbits connected by magnetic breakdown. The state of the art of this problematics is reviewed.

cond-mat.str-el↗

arXiv2012

Quantum oscillations in the linear chain of coupled orbits: the organic metal with two cation layers theta-(ET)(4)CoBr(4)(C(6)H(4)Cl(2))

Analytical formulae for de Haas-van Alphen (dHvA) oscillations in linear chain of coupled two-dimensional (2D) orbits (Pippard's model) are derived systematically taking into account the chemical potential oscillations in magnetic field. Although corrective terms are observed, basic (alpha) and magnetic breakdown-induced (beta and 2beta - alpha) orbits can be accounted for by the Lifshits-Kosevich (LK) and Falicov-Stachowiak semiclassical models in the explored field and temperature ranges. In contrast, the 'forbidden orbit' beta - alpha amplitude is described by a non-LK equation involving a product of two classical orbit amplitudes. Furthermore, strongly non-monotonic field and temperature dependence may be observed for the second harmonics of basic frequencies such as 2alpha and the magnetic breakdown orbit beta + alpha, depending on the value of the spin damping factors. These features are in agreement with the dHvA oscillation spectra of the strongly 2D organic metal theta- theta-(ET)(4)CoBr(4)(C(6)H(4)Cl(2)).

cond-mat.str-el↗

arXiv2011

Emergence of skew distributions in controlled growth processes

Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the evolution quation, to obtain such skew distributions as power-law, log-normal, and Weibull distributions, depending on the growth or division and production. Specifically, repeated production of elements of uniform size leads to power-law distributions, whereas production of elements with the size distributed according to the current distribution as well as no production of new elements results in log-normal distributions. Finally, division into two, or binary fission, bears Weibull distributions. Numerical simulations are also carried out, confirming the validity of the obtained solutions.

cond-mat.stat-mech↗

arXiv2011

Weibull-type limiting distribution for replicative systems

The Weibull function is widely used to describe skew distributions observed in nature. However, the origin of this ubiquity is not always obvious to explain. In the present paper, we consider the well-known Galton-Watson branching process describing simple replicative systems. The shape of the resulting distribution, about which little has been known, is found essentially indistinguishable from the Weibull form in a wide range of the branching parameter; this can be seen from the exact series expansion for the cumulative distribution, which takes a universal form. We also find that the branching process can be mapped into a process of aggregation of clusters. In the branching and aggregation process, the number of events considered for branching and aggregation grows cumulatively in time, whereas, for the binomial distribution, an independent event occurs at each time with a given success probability.

physics.data-an↗

arXiv2010

Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval-particle method

The one-dimensional coagulation-diffusion process describes the strongly fluctuating dynamics of particles, freely hopping between the nearest-neighbour sites of a chain such that one of them disappears with probability 1 if two particles meet. The exact two-time correlation and response function in the one-dimensional coagulation-diffusion process are derived from the empty-interval-particle method. The main quantity is the conditional probability of finding an empty interval of n consecutive sites, if at distance d a site is occupied by a particle. Closed equations of motion are derived such that the probabilities needed for the calculation of correlators and responses, respectively, are distinguished by different initial and boundary conditions. In this way, the dynamical scaling of these two-time observables is analysed in the longtime ageing regime. A new generalised fluctuation-dissipation ratio with an universal and finite limit is proposed.

cond-mat.stat-mech↗

arXiv2010

Exact correlations in the one-dimensional coagulation-diffusion process by the empty-interval method

The long-time dynamics of reaction-diffusion processes in low dimensions is dominated by fluctuation effects. The one-dimensional coagulation-diffusion process describes the kinetics of particles which freely hop between the sites of a chain and where upon encounter of two particles, one of them disappears with probability one. The empty-interval method has, since a long time, been a convenient tool for the exact calculation of time-dependent particle densities in this model. We generalise the empty-interval method by considering the probability distributions of two simultaneous empty intervals at a given distance. While the equations of motion of these probabilities reduce for the coagulation-diffusion process to a simple diffusion equation in the continuum limit, consistency with the single-interval distribution introduces several non-trivial boundary conditions which are solved for the first time for arbitrary initial configurations. In this way, exact space-time-dependent correlation functions can be directly obtained and their dynamic scaling behaviour is analysed for large classes of initial conditions.

cond-mat.stat-mech↗

arXiv2009

Grassmann techniques applied to classical spin systems

We review problems involving the use of Grassmann techniques in the field of classical spin systems in two dimensions. These techniques are useful to perform exact correspondences between classical spin Hamiltonians and field-theory fermionic actions. This contributes to a better understanding of critical behavior of these models in term of non-quadratic effective actions which can been seen as an extension of the free fermion Ising model. Within this method, identification of bare masses allows for an accurate estimation of critical points or lines and which is supported by Monte-Carlo results and diagrammatic techniques.

cond-mat.stat-mech↗

arXiv2009

Random walks and magnetic oscillations in compensated metals

The field- and temperature-dependent de Haas-van Alphen oscillations spectrum is studied for an ideal two-dimensional compensated metal whose Fermi surface is made of a linear chain of successive orbits with electron and hole character, coupled by magnetic breakdown. We show that the first harmonics amplitude can be accurately evaluated on the basis of the Lifshits-Kosevich (LK) formula by considering a set of random walks on the orbit network, in agreement with the numerical resolution of semi-classical equations. Oppositely, the second harmonics amplitude does not follow the LK behavior and vanishes at a critical value of the field-to-temperature ratio which depends explicitly on the relative value between the hole and electron effective masses.

cond-mat.str-el↗

arXiv2008

Alternative description of the 2D Blume-Capel model using Grassmann algebra

We use Grassmann algebra to study the phase transition in the two-dimensional ferromagnetic Blume-Capel model from a fermionic point of view. This model presents a phase diagram with a second order critical line which becomes first order through a tricritical point, and was used to model the phase transition in specific magnetic materials and liquid mixtures of He$^3$-He$^4$. In particular, we are able to map the spin-1 system of the BC model onto an effective fermionic action from which we obtain the exact mass of the theory, the condition of vanishing mass defines the critical line. This effective action is actually an extension of the free fermion Ising action with an additional quartic interaction term. The effect of this term is merely to render the excitation spectrum of the fermions unstable at the tricritical point. The results are compared with recent numerical Monte-Carlo simulations.

cond-mat.stat-mech↗

arXiv2008

Second-order critical lines of spin-S Ising models in a splitting field with Grassmann techniques

We propose a method to study the second-order critical lines of classical spin-$S$ Ising models on two-dimensional lattices in a crystal or splitting field, using an exact expression for the bare mass of the underlying field theory. Introducing a set of anticommuting variables to represent the partition function, we derive an exact and compact expression for the bare mass of the model including all local multi-fermions interactions. By extension of the Ising and Blume-Capel models, we extract the free energy singularities in the low momentum limit corresponding to a vanishing bare mass. The loci of these singularities define the critical lines depending on the spin S, in good agreement with previous numerical estimations. This scheme appears to be general enough to be applied in a variety of classical Hamiltonians.

cond-mat.stat-mech↗

arXiv2008

Damping of field-induced chemical potential oscillations in ideal two-band compensated metals

The field and temperature dependence of the de Haas-van Alphen oscillations spectrum is studied for an ideal two-dimensional compensated metal. It is shown that the chemical potential oscillations, involved in the frequency combinations observed in the case of uncompensated orbits, are strongly damped and can even be suppressed when the effective masses of the electron- and hole-type orbits are the same. When magnetic breakdown between bands occurs, this damping is even more pronounced and the Lifshits-Kosevich formalism accounts for the data in a wide field range.

cond-mat.stat-mech↗

arXiv2006

Origin of the approximate universality of distributions in equilibrium correlated systems

We propose an interpretation of previous experimental and numerical experiments, showing that for a large class of systems, distributions of global quantities are similar to a distribution originally obtained for the magnetization in the 2D-XY model . This approach, developed for the Ising model, is based on previous numerical observations. We obtain an effective action using a perturbative method, which successfully describes the order parameter fluctuations near the phase transition. This leads to a direct link between the D-dimensional Ising model and the XY model in the same dimension, which appears to be a generic feature of many equilibrium critical systems and which is at the heart of the above observations.

cond-mat.stat-mech↗

arXiv2005

Boundary field induced first order transition in the 2D Ising model: Exact study

We present in this paper an exact study concerning a first order transition induced by an inhomogeneous boundary magnetic field in the 2D Ising model. From a previous analysis of the interfacial free energy in the discrete case (J. Phys. A, 2849, 2005), we identify, using an asymptotic expansion in the thermodynamic limit, the transition line that separates the regime where the interface is localised near the boundary from the regime where it is propagating inside the bulk. In particular, the critical line has a strong dependence on the aspect ratio of the lattice.

cond-mat.stat-mech↗

arXiv2005

Asymptotic behavior of the density of states on a random lattice

We study the diffusion of a particle on a random lattice with fluctuating local connectivity of average value q. This model is a basic description of relaxation processes in random media with geometrical defects. We analyze here the asymptotic behavior of the eigenvalue distribution for the Laplacian operator. We found that the localized states outside the mobility band and observed by Biroli and Monasson (1999, J. Phys. A: Math. Gen. 32 L255), in a previous numerical analysis, are described by saddle point solutions that breaks the rotational symmetry of the main action in the real space. The density of states is characterized asymptotically by a series of peaks with periodicity 1/q.

cond-mat.dis-nn↗

arXiv2005

1D action and partition function for the 2D Ising model with boundary magnetic field

In this article we obtain some exact results for the 2D Ising model with a general boundary magnetic field and for a finite size system, by an alternative method to that developed by B. McCoy and T.T. Wu. This method is a generalization of ideas from V.N. Plechko presented for the 2D Ising model in zero field, based on the representation of the Ising model using a Grassmann algebra. In this way, a Gaussian 1D action is obtained for a general configuration of the boundary magnetic field. In the special case where the magnetic field is homogeneous, we check that our results are in agreement with McCoy and Wu's previous work, and we also compute the two point correlation functions on the boundary. We use this correlation function to obtain the exact partition function and the free energy in the special case of an inhomogeneous boundary magnetic field.

cond-mat.stat-mech↗

arXiv2004

Criterion for universality class independent critical fluctuations: example of the 2D Ising model

Order parameter fluctuations for the two dimensional Ising model in the region of the critical temperature are presented. A locus of temperatures T*(L) and of magnetic fields B*(L) are identified, for which the probability density function is similar to that for the 2D-XY model in the spin wave approximation.The characteristics of the fluctuations along these points are largely independent of universality class. We show that the largest range of fluctuations relative to the variance of the distribution occurs along these loci of points, rather than at the critical temperature itself and we discuss this observation in terms of intermittency. Our motivation is the identification of a generic form for fluctuations in correlated systems in accordance with recent experimental and numerical observations. We conclude that a universality class dependent form for the fluctuations is a particularity of critical phenomena related to the change in symmetry at a phase transition.

cond-mat.stat-mech↗