Critical exponents of Manhattan Hamiltonian walks in two dimensions,from Potts andO(n) models

We consider a set of Hamiltonian circuits filling a Manhattan lattice, i.e., a square lattice with alternating traffic regulation. We show that the generating function (with fugacityz) of this set is identical to the critical partition function of aq-state Potts model on an unoriented square lattice withq ^1/2 =z. The set of critical exponents governing correlations of Hamiltonian circuits is derived using a Coulomb gas technique. These exponents are also found to be those of an O(n) vector model in the low-temperature phase withn =q ^1/2 =z. The critical exponents in the limitz = 0 are then those of spanning trees (q= 0) and of dense polymers (n=0,T < T_c), corresponding to a conformal theory with central chargeC = –2. This shows that the Manhattan orientation and the Hamiltonian constraint of filling all the lattice are irrelevant for the infrared critical properties of Hamiltonian walks.     

Geometrical construction of a generalized Skyrme Lagrangian

A geometrical scheme is proposed that leads to a straightforward generalization of a Skyrme Lagrangian, comprising higher-order terms up to the eighth power in pion fields.Boursière DGRST.     

Magnetic ordering in FexMg1−xCl2, (x=0.55, x=0.45, x=0.30)

Mössbauer measurements on the diluted crystals Fe_xMg_1–xCl₂ show that fluctuating magnetic clusters are present. These can be related to the known spin-glass properties of these compounds. The fluctuating frequencies depend on temperature and the fluctuations can be suppressed by a sufficiently high external magnetic field     

Two local search approaches for solving real-life car sequencing problems

The NP-hard problem of car sequencing appears as the heart of the logistic process of many car manufacturers. The subject of the ROADEF’2005 challenge addressed a car sequencing problem proposed by the car manufacturer RENAULT, more complex than the academic problem generally addressed in the literature. This paper describes two local search approaches for this problem. In the first part, a new approach by very large-scale neighborhood search is presented. This approach, designed during the qualification stage preceding the final, is based on an original integer linear programming formulation. The second part is dedicated to the approach which enabled us to win the ROADEF’2005 challenge. Inspired by the latest works on the subject, this one is based on very fast explorations of small neighborhoods. Our contribution here is mainly algorithmic, in particular by showing how much exploiting invariants speeds up the neighborhood evaluation and contributes to the diversification of the search. Finally, the two approaches are compared and discussed through an extensive computational study on RENAULT’s benchmarks. The main conclusion drawn at this point is that sophisticated metaheuristics are useless to solve car sequencing problems. More generally, our victory on ROADEF’2005 challenge demonstrates that algorithmic aspects, sometimes neglected, remain the key ingredients for designing and engineering high-performance local search heuristics.     

Distribution of crystal electric fields in amorphous rare-earth alloys

We report magnetic measurements on extensive series of amorphous alloys containing small concentrations of rare-earths. We find that the magnetic properties of the rare-earth ions are strongly affected by crystal-field effects, particularly for non-Kramers ion such as Pr (J = 4), Tb and Tm (J = 6). Our results cannot be accounted for in models based on simple uniaxial crystal fields. Their analysis in a more general model of quadratic crystal field allows us to derive the distribution of the asymmetry parameter η. Finally we discuss the change of the magnetic behavior and of the local symmetry distribution induced by a structural relaxation of our alloys.