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R. Mélin

Publications and source records attributed to R. Mélin.

66 records · Page 4Linked to original sources
arXiv1997

A single chain analysis of doped quasi one dimensional spin 1 compounds: paramagnetic versus spin 1/2 doping

We present a numerical study of single chain models of doped spin 1 compounds. We use low energy effective one-dimensional models for both the cases of paramagnetic and spin-1/2 doping. In the case of paramagnetic doping, the effective model is equivalent to the bond disordered spin-1/2 chain model recently analyzed by means of real space renormalization group by Hyman and Yang. By means of exact diagonalizations in the XX limit, we confirm the stability of the Haldane phase for weak disorder. Above a critical amount of disorder, the effective model flows to the so called random singlet fixed point. In the case of spin-1/2 doping, we argue that the Haldane phase should be destabilized even for weak disorder. This picture is not in contradiction with existing experimental data. We also discuss the possible occurrence of (unobserved) antiferromagnetically ordered phases.

cond-mat↗
arXiv1997

A theoretical investigation of the specific heat of superlattices in a magnetic field

We analyze the specific heat variations as a function of an external magnetic field of a simple model of superlattice that includes (i) in--plane ferromagnetic exchange, (ii) interplane ferromagnetic exchange, (iii) dipolar interactions, (iv) magnetocristalline anisotropy. The calculations are carried out at the spin wave level. The interplay between the existence of a canting transition and the anisotropy of the structure generates non trivial behavior for the spin wave contribution to the low temperature specific heat as a function of an external magnetic field when dipolar interactions and magnetocristalline anisotropy are taken into account.

cond-mat↗
arXiv1997

Enhanced magnetic fluctuations in doped spin-Peierls systems: a single-chain model analysis

We analyze by means of real space Renormalization Group (RG) as well as by exact diagonalizations the properties of a single-chain model of a doped spin-Peierls system, where a major role is played by the localized moments created by the impurities. We are able to follow analytically the RG flow, which allows us to determine the relevant cross-over temperatures. In particular, we find an enhancement of magnetic correlations due to disorder, coexisting with an underlying dimerization, in an intermediate temperature range below the spin-Peierls critical temperature and above the coherence temperature of a regular array built by those localized moments (so-called soliton bandwidth). The possible relevance of these results to the doped inorganic spin-Peierls compound CuGeO$_3$ is discussed.

cond-mat↗
arXiv1997

Coexistence of antiferromagnetism and dimerization in a disordered spin-Peierls model: exact results

A model of disordered spin-Peierls system is considered, where domain walls are randomly distributed as a telegraph noise. For this realization of the disorder in an XX spin chain, we calculate exactly the density of states as well as several thermodynamic quantities. The resulting physical behavior should be qualitatively unchanged even for an XXZ chain, up to the isotropic XXX point. For weak disorder, besides a high energy regime where the behavior of a pure spin-Peierls system is recovered, there is a cross-over to a low energy regime with singular thermodynamic properties and enhanced antiferromagnetic fluctuations. These regimes are analyzed with the help of exact results, and the relevant energy scales determined. We discuss the possible relevance of such a disorder realization to the doped inorganic spin-Peierls compound CuGeO$_3$.

cond-mat.str-el↗
arXiv1997

Glauber Dynamics and Ageing

The Glauber dynamics of various models (REM-like trap models, Brownian motion, BM model, Ising chain and SK model) is analyzed in relation with the existence of ageing. From a finite size Glauber matrix, we calculate a time $τ_w(N)$ after which the system has relaxed to the equilibrium state. The case of metastability is also discussed. If the only non zero overlaps between pure states are only self-overlaps (REM-like trap models, BM model), the existence or absence of ageing depends only on the behavior of the density of eigenvalues for small eigenvalues. We have carried out a detailed numerical and analytical analysis of the density of eigenvalues of the REM-like trap models. In this case, we show that the behavior of the density of eigenvalues for typical trap realizations is related to the spectral dimension of the equivalent random walk model.

cond-mat↗
arXiv1996

nu=1/2 quantum Hall effect in the Aharonov-Casher geometry in a mesoscopic ring

We study the effect of an electric charge in the middle of a ring of electrons in a magnetic field such as $ν= 1/2$. In the absence of the central charge, a residual current should appear due to an Aharanov-Bohm effect. As the charge varies, periodic currents should appear in the ring. We evaluate the amplitude of these currents, as well as their period as the central charge varies. The presence of these currents should be a direct signature of the existence of a statistical gauge field in the $ν=1/2$ quantum Hall effect. Numerical diagonalizations for a small number of electrons on the sphere are also carried out. The numerical results up to 9 electrons are qualitatively consistent with the mean field picture.

cond-mat.mes-hall↗
arXiv1996

Magnetization Distribution on Fractals and Percolation Lattices

We study the magnetization distribution of the Ising model on two regular fractals (a hierarchical lattice, the regular simplex) and percolation clusters at the percolation threshold in a two dimensional imbedding space. In all these cases, the only fixed point is $T=0$. In the case of the two regular fractals, we show that the magnetization distribution is non trivial below $T^{*} \simeq A^{*}/n$, with $n$ the number of iterations, and $A^{*}$ related to the order of ramification. The cross-over temperature $T^{*}$ is to be compared with the glass cross-over temperature $T_g \simeq A_g/n$. An estimation of the ratio $T^{*}/T_g$ yields an estimation of the order of ramification of bidimensional percolation clusters at the threshold ($C = 2.3 \pm 0.2$).

cond-mat↗
arXiv1996

Magnetic field relaxation in ferromagnetic Ising systems

We analyze the thermal magnetization reversal processes in magnetic grains. Two experiments are carried out: swtiching time and switching field experiments. In both cases, we find that the simulated behavior is coherent with existing experimental data (the streched exponent of the switching time experiment increases with the temperature and is superior to unity; there exists a master curve for the switching field experiment). Moreover, we simulated magnetic grains in a region of parameters where no experimental data are available. We find that the relaxation time distribution $P(\lnτ)$ is gaussian, and we find the existence of a strong field regime.

cond-mat↗
arXiv1996

Glauber dynamics in a zero magnetic field and eigenvalue spacing statistics

We discuss the eigenvalue spacing statistics of the Glauber matrix for various models of statistical mechanics (a one dimensional Ising model, a two dimensional Ising model, a one dimensional model with a disordered ground state, and a SK model with and without a ferromagnetic bias). The dynamics of the one dimensional Ising model are integrable, and the eigenvalue spacing statistics are non-universal. In the other cases, the eigenvalue statistics in the high temperature regime are intermediate between Poisson and G.O.E (with $P(0)$ of the order of $0.5$). In the intermediate temperature regime, the statistics are G.O.E.. In the low temperature regime, the statistics have a peak at $s=0$. In the low temperature regime, and for disordered systems, the eigenvalues condense around integers, due to the fact that the local field on any spin never vanishes. This property is still valid for the Ising model on the Cayley tree, even if it is not disordered. We also study the spacing between the two largest eigenvalues as a function of temperature. This quantity seems to be sensitive to the existence of a broken symmetry phase.

cond-mat↗
arXiv1995

Level spacing statistics of bidimensional Fermi liquids: II. Landau fixed point and quantum chaos

We investigate the presence of quantum chaos in the spectrum of the bidimensional Fermi liquid by means of analytical and numerical methods. This model is integrable in a certain limit by bosonization of the Fermi surface. We study the effect on the level statisticsof the momentum cutoff $Λ$ present in the bidimensional bosonization procedure. We first analyse the level spacing statistics in the $Λ$-restricted Hilbert space in one dimension. With $g_2$ and $g_4$ interactions, the level statistics are found to be Poissonian at low energies, and G.O.E. at higher energies, for a given cut-off $Λ$. In order to study this cross-over, a finite temperature is introduced as a way of focussing, for a large inverse temperature $β$, on the low energy many-body states, and driving the statistics from G.O.E. to Poissonian. As far as two dimensions are concerned, we diagonalize the Fermi liquid Hamiltonian with a small number of orbitals. The level spacing statistics are found to be Poissonian in the $Λ$-restricted Hilbert space, provided the diagonal elements are of the same order of magnitude as the off-diagonal matrix elements of the Hamiltonian.

cond-mat↗
arXiv1993

Breakdown of the Fermi Liquid picture in one dimensional fermion systems: connection with the energy level statistics

Using the adiabatic switching of interactions, we establish a condition for the existence of electronic quasiparticles in a Luttinger liquid. It involves a characteristic interaction strength proportional to the inverse square root of the system length. An investigation of the exact energy level separation probability distribution shows that this interaction scale also corresponds to a cross-over from the non interacting behaviour to a rather typical case for integrable systems, namely an exponential distribution. The level spacing statistics of a spin $1/2$, one branch Luttinger model are also analyzed, as well as the level statistics of a two coupled chain model.

cond-mat↗