)l) and L. M. FALICOV (a)2)The contribution of Bloch-wall electron-scattering to the electrical resistivity of a ferromagnetic metal is calculated. Calculations are carried out for various cases which include small as well as large exchange splittings. In all cases, spherical Fermi surfaces are considered, the wall width is assumed to be small compared to the intrinsic electron mean-freepath and diamagnetic effects are neglected. It is found t h a t the experimental results (large negative magnetoresistance between 0 and 100 G ) could be explained, even when diamagnetic effects are not included, if the majority and minority spins have sizeably different density-of-states a t the Fermi level.Der Anteil der Elektronenstreuung an Blochwanden zum elektrischen Widerstand in Ferromagneten wird berechnet. Die Rechnungen werden fur verschiedene Falle mit sowohl kleiner als auch groBer Austauschwechselwirkung durchgefuhrt. I n allen Flllen wird kugelformige Gestalt der Fermioberflachen vorausgesetzt, die Wanddicke wird als klein angenommen gegenuber der naturlichen mittleren freien Weglange der Elektronen, und diamagnetische Effekte werden vernachliissigt. Experimentelle Ergebnisse -groBer negativer Magnetowiderstand fur Felder kleiner als 100 G -konnen erklairt werden, falls Majoritatsund Minoritatsspins erheblich voneinander abweichende Zustandsdichten an der Fermienergie aufweisen, selbst dann, wenn diamagnetische Effekte nicht berucksichtigt werden.

We explore the physical properties of a unified microscopic theory for the coexistence of superconductivity and charge-density waves ͑CDWs͒ in two-dimensional transition-metal dichalcogenides. In the case of particlehole symmetry, the elementary particles are Dirac fermions at the nodes of the charge density wave gap. When particle-hole symmetry is broken, electron ͑hole͒ pockets are formed around the Fermi surface. The superconducting ground state emerges from the pairing of nodal quasiparticles mediated by acoustic phonons via a piezoelectric coupling. We calculate several properties in the s-wave superconducting phase, including specific heat, ultrasound absorption, nuclear magnetic relaxation ͑NMR͒, and thermal and optical conductivities. In the case with particle-hole symmetry, the specific-heat jump at the transition deviates strongly from ordinary superconductors. The NMR response shows an anomalous anisotropy due to the broken time-reversal symmetry of the superconducting gap, induced by the triple CDW state. The loss of the lattice inversion center in the CDW phase leads to anomalous coherence factors in the optical conductivity and to the appearance of an absorption edge at the optical gap energy. In addition, optical and thermal conductivities display anomalous peaks in the infrared when particle-hole symmetry is broken.

Boundary conditions monitor the finite-size dependence of scaling functions for the Ising model. We study the low-temperature phase for the extremely anisotropic limit, or quantum version of the 2D classical Ising model, by means of combined exact results and large-size numerical calculations. The mass gap (inverse of correlation length) is the suitable order parameter for the finite system, and its finite-size behavior is studied as a function of variable boundary conditions. We find that the well-known exponential convergence to zero of the mass gap is only valid in a limited range of pararneters; it strikingly changes into a power law for antiperiodic boundary conditions. We suggest that this puzzling phenomenon is associated with topological excitations.