Higher-order Spin Research Articles

Perpendicular Susceptibility of the Ising Model

A high-temperature expansion of the partition function for a lattice of N spins with Hamiltonian H=−J ∑ (ij)σizσjz−mHz ∑ iσiz−mHx ∑ iσixis derived and thence an expansion for the zero-field perpendicular susceptibility is found. By perturbation theory, χ⊥(T) is also expanded at low temperatures and seen, in general, to increase with T from the value χ⊥(O) = Nm2/q | J |, where q is the coordination number of the lattice. The perpendicular susceptibility is re-expressed in terms of near neighbor pair and higher-order spin correlation functions in zero field. This yields exact closed formulas for the linear chain, the Bethe pseudolattices, and for the plane square and honeycomb lattices. The behavior of χ⊥(T) in the critical region is investigated for these lattices and for the plane superexchange lattice.

Investigation of Spinning Detonation and Detonation Stability

The stability of a detonation wave and the nature of a spinning detonation have been investigated by observing the patterns inscribed by the wave in soot coatings on films located on the circumference of the detonation tube and on the end plate. The detonation instability reported by others persists to an initial pressure of over 2 atm and to wave velocities at least 75% greater than the equilibrium value. The wave front of a simple spinning detonation contains a complex Mach interaction with wave inclinations as high as 37° to the tube diameter. The acoustic theory of spinning detonation does describe high-order spin if it is assumed that two or more modes of vibration coexist.