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