Laurent Pierre

Consistency of maximum-likelihood and variational estimators in the Stochastic Block Model

The stochastic block model (SBM) is a probabilistic model de- signed to describe heterogeneous directed and undirected graphs. In this paper, we address the asymptotic inference on SBM by use of maximum- likelihood and variational approaches. The identi ability of SBM is proved, while asymptotic properties of maximum-likelihood and variational esti- mators are provided. In particular, the consistency of these estimators is settled, which is, to the best of our knowledge, the rst result of this type for variational estimators with random graphs.

Magnetothermodynamics of the spin- 1 / 2 Kagome antiferromagnet

In this paper, we use a new hybrid method to compute the thermodynamic behavior of the spin- 1 / 2 Kagome antiferromagnet under the influence of a large external magnetic field. We find a T2 low-temperature behavior and a very low sensitivity of the specific heat to a strong external magnetic field. We display clear evidence that this low-temperature magnetothermal effect is associated with the existence of low-lying fluctuating singlets, but also that the whole picture ( T2 behavior of C(v) and the thermally activated spin susceptibility) implies contribution of both nonmagnetic and magnetic excitations. Comparison with experiments is made.

Determination of the exchange energies in Li2VOSiO4from a high-temperature series analysis of the square-lattice J1-J2 Heisenberg model

We present a high-temperature expansion (HTE) of the magnetic susceptibility and specific heat data of Melzi et al. on Li 2 VOSiO 4 [Phys. Rev. B 64, 024409 (2001)]. The data are very well reproduced by the J 1 -J 2 Heisenberg model on the square lattice with exchange energies J 1 =1.25′0.5 K and J 2 =5.95′0.2 K. The maximum of the specific heat C m a x υ (T m a x ) is obtained as a function of J 2 /J 1 from an improved method based on HTE.

J1-J2 QUANTUM HEISENBERG ANTIFERROMAGNET ON THE TRIANGULAR LATTICE : A GROUP-SYMMETRY ANALYSIS OF ORDER BY DISORDER

On the triangular lattice, for

Model for Heterogeneous Random Networks Using Continuous Latent Variables and an Application to a Tree–Fungus Network

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Chirality and Z2 vortices in a Heisenberg spin model on the kagome lattice

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Néel order versus spin liquid in quantum Heisenberg antiferromagnets on triangular and Kagomé lattices

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Quantum Antiferromagnets: From Néel Ordered Groundstates to Spin Liquids

between 1/8 and 1, the classical Heisenberg model with first- and second-neighbor interactions presents four-sublattice ordered ground states. Spin-wave calculations of Chubukov and Jolicoeur and Korshunov suggest that quantum fluctuations select amongst these states a collinear two-sublattice order. From theoretical requirements, we develop the full symmetry analysis of the low-lying levels of the spin-1/2 Hamiltonian in the hypotheses of either a four- or a two-sublattice order. We show on the exact spectra of periodic samples (N=12, 16, and 28) how quantum fluctuations select the collinear order from the four-sublattice order.

Broken symmetries and thermodynamic limit in quantum antiferromagnets

The mixture model is a method of choice for modeling heterogeneous random graphs, because it contains most of the known structures of heterogeneity: hubs, hierarchical structures, or community structure. One of the weaknesses of mixture models on random graphs is that, at the present time, there is no computationally feasible estimation method that is completely satisfying from a theoretical point of view. Moreover, mixture models assume that each vertex pertains to one group, so there is no place for vertices being at intermediate positions. The model proposed in this article is a grade of membership model for heterogeneous random graphs, which assumes that each vertex is a mixture of extremal hypothetical vertices. The connectivity properties of each vertex are deduced from those of the extreme vertices. In this new model, the vector of weights of each vertex are fixed continuous parameters. A model with a vector of parameters for each vertex is tractable because the number of observations is proportional to the square of the number of vertices of the network. The estimation of the parameters is given by the maximum likelihood procedure. The model is used to elucidate some of the processes shaping the heterogeneous structure of a well-resolved network of host/parasite interactions.

Rational index of vector addition systems languages

The phase diagram of the classical J1–J2 model on the kagome lattice is investigated by using extensive Monte Carlo simulations. In a realistic range of parameters, this model has a low-temperature chiral-ordered phase without long-range spin order. We show that the critical transition marking the destruction of the chiral order is preempted by the first-order proliferation of Z2 point defects. The core energy of these vortices appears to vanish when approaching the T=0 phase boundary, where both Z2 defects and gapless magnons contribute to disordering the system at very low temperatures. This situation might be typical of a large class of frustrated magnets. Possible relevance for real materials is also discussed.