arXiv subjects

B. Berche

Publications and source records attributed to B. Berche.

46 records · Page 3Linked to original sources

arXiv2002

Correlations in the low-temperature phase of the two-dimensional XY model

Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with fixed boundary conditions. Using a conformal mapping it is very easy to deduce the exponent eta_sigma(T) of the order parameter correlation function at any temperature in the critical phase of the model. The temperature behaviour of eta_sigma(T) is obtained numerically with a good accuracy up to the Kosterlitz-Thouless transition temperature. At very low temperatures, a good agreement is found with Berezinskii's harmonic approximation. Surprisingly, we show some evidence that there are no logarithmic corrections to the behaviour of the order parameter density profile (with symmetry breaking surface fields) at the Kosterlitz-Thouless transition temperature.

cond-mat.stat-mech↗

arXiv2002

Crossover effects in the bond-diluted Ising model in three dimensions

We investigate by Monte Carlo simulations the critical properties of the three-dimensional bond-diluted Ising model. The phase diagram is determined by locating the maxima of the magnetic susceptibility and is compared to mean-field and effective-medium approximations. The calculation of the size-dependent effective critical exponents shows the competition between the different fixed points of the model as a function of the bond dilution.

cond-mat.stat-mech↗

arXiv2001

Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model

We consider m two-dimensional semi-infinite planes of Ising spins joined together through surface spins and study the critical behaviour near to the junction. The m=0 limit of the model - according to the replica trick - corresponds to the semi-infinite Ising model in the presence of a random surface field (RSFI). Using conformal mapping, second-order perturbation expansion around the weakly- and strongly-coupled planes limits and differential renormalization group, we show that the surface critical behaviour of the RSFI model is described by Ising critical exponents with logarithmic corrections to scaling, while at multiple junctions (m>2) the transition is first order. There is a spontaneous junction magnetization at the bulk critical point.

cond-mat.stat-mech↗

arXiv2001

Size effect on magnetism of Fe thin films in Fe/Ir superlattices

In ferromagnetic thin films, the Curie temperature variation with the thickness is always considered as continuous when the thickness is varied from $n$ to $n+1$ atomic planes. We show that it is not the case for Fe in Fe/Ir superlattices. For an integer number of atomic planes, a unique magnetic transition is observed by susceptibility measurements, whereas two magnetic transitions are observed for fractional numbers of planes. This behavior is attributed to successive transitions of areas with $n$ and $n+1$ atomic planes, for which the $T_c$'s are not the same. Indeed, the magnetic correlation length is presumably shorter than the average size of the terraces. Monte carlo simulations are performed to support this explanation.

cond-mat.mtrl-sci↗

arXiv1997

Surface Magnetization of Aperiodic Ising Quantum Chains

We study the surface magnetization of aperiodic Ising quantum chains. Using fermion techniques, exact results are obtained in the critical region for quasiperiodic sequences generated through an irrational number as well as for the automatic binary Thue-Morse sequence and its generalizations modulo p. The surface magnetization exponent keeps its Ising value, beta_s=1/2, for all the sequences studied. The critical amplitude of the surface magnetization depends on the strength of the modulation and also on the starting point of the chain along the aperiodic sequence.

cond-mat.stat-mech↗

arXiv1997

Marginal Extended Perturbations in Two Dimensions and Gap-Exponent Relations

The most general form of a marginal extended perturbation in a two-dimensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surface, a line or a point for which exact results have been previously obtained. The first-order corrections to the local exponents, which are functions of the amplitude of the defect, are deduced from a perturbation expansion of the two-point correlation functions. Assuming covariance under conformal transformation, the perturbed system is mapped onto a cylinder. Working in the Hamiltonian limit, the first-order corrections to the lowest gaps are calculated for the Ising model. The results confirm the validity of the gap-exponent relations for the perturbed system.

hep-th↗

arXiv1997

Surface Magnetization of Aperiodic Ising Systems: a Comparative Study of the Bond and Site Problems

We investigate the influence of aperiodic perturbations on the critical behaviour at a second order phase transition. The bond and site problems are compared for layered systems and aperiodic sequences generated through substitution. In the bond problem, the interactions between the layers are distributed according to an aperiodic sequence whereas in the site problem, the layers themselves follow the sequence. A relevance-irrelevance criterion introduced by Luck for the bond problem is extended to discuss the site problem. It involves a wandering exponent for pairs, which can be larger than the one considered before in the bond problem. The surface magnetization of the layered two-dimensional Ising model is obtained, in the extreme anisotropic limit, for the period-doubling and Thue-Morse sequences.

cond-mat.stat-mech↗

arXiv1997

Surface Magnetization and Critical Behavior of Aperiodic Ising Quantum Chains

We consider semi-infinite two-dimensional layered Ising models in the extreme anisotropic limit with an aperiodic modulation of the couplings. Using substitution rules to generate the aperiodic sequences, we derive functional equations for the surface magnetization. These equations are solved by iteration and the surface magnetic exponent can be determined exactly. The method is applied to three specific aperiodic sequences, which represent different types of perturbation, according to a relevance-irrelevance criterion. On the Thue-Morse lattice, for which the modulation is an irrelevant perturbation, the surface magnetization vanishes with a square root singularity, like in the homogeneous lattice. For the period-doubling sequence, the perturbation is marginal and the surface magnetic exponent varies continuously with the modulation amplitude. Finally, the Rudin-Shapiro sequence, which corresponds to the relevant case, displays an anomalous surface critical behavior which is analyzed via scaling considerations: Depending on the value of the modulation, the surface magnetization either vanishes with an essential singularity or remains finite at the bulk critical point, i.e., the surface phase transition is of first order.

cond-mat.stat-mech↗

arXiv1997

Marginal Anisotropy in Layered Aperiodic Ising Systems

Two-dimensional layered aperiodic Ising systems are studied in the extreme anisotropic limit where they correspond to quantum Ising chains in a transverse field. The modulation of the couplings follows an aperiodic sequence generated through substitution. According to Luck's criterion, such a perturbation becomes marginal when the wandering exponent of the sequence vanishes. Three marginal sequences are considered: the period-doubling, paper-folding and three-folding sequences. They correspond to bulk perturbations for which the critical temperature is shifted. The surface magnetization is obtained exactly for the three sequences. The scaling dimensions of the local magnetization on both surfaces vary continuously with the modulation factor. The low-energy excitations of the quantum chains are found to scale as L^z with the size L of the system. This is the behaviour expected for a strongly anisotropic system, where z is the ratio of the exponents of the correlation lengths in the two directions. The anisotropy exponent z is equal to the sum of the scaling dimensions of the local magnetization on the two surfaces. The anisotropic scaling behaviour is verified numerically for other surface and bulk critical properties as well.

cond-mat.stat-mech↗

arXiv1997

Anisotropic Scaling in Layered Aperiodic Ising Systems

The influence of a layered aperiodic modulation of the couplings on the critical behaviour of the two-dimensional Ising model is studied in the case of marginal perturbations. The aperiodicity is found to induce anisotropic scaling. The anisotropy exponent z, given by the sum of the surface magnetization scaling dimensions, depends continuously on the modulation amplitude. Thus these systems are scale invariant but not conformally invariant at the critical point.

cond-mat.stat-mech↗