High Temperature Dynamics of the Linear Chain Spin -One Model in a Transverse Field

Isao Harada, Norihiro Otsuka, Keiji Fukui +7 more

Jiahao Yang, Márton Kormos, Jianda Wu +1 more

J. Oitmaa, Michael Plischke, T.A. Winchester

We derive the moments, at $T=\ensuremath{\infty}$, of the longitudinal spin-spin correlation function of the Ising model in a transverse field. The first 20 moments are obtained for the linear chain, the first 12 moments for the fcc lattice. We use a method of Nickel [J. Phys. C 7, 1719 (1914)] to construct the relaxation function and find excellent agreement with the exact results of Capel and Perk [Physica (Utrecht) 87A, 211 (1977)] in one dimension and extremely good convergence in three dimensions. Our method of analysis provides much better convergence than methods based on truncation of the continued-fraction representation.

Sergei A. Pikin, V. M. Tsukernik

Oleg Derzhko, Taras Krokhmalskii

We have considered a numerical scheme for the calculation of the equilibrium properties of spin-1/2 XY chains. Within its frames it is necessary to solve in the last resort only the 2N\times 2N eigenvalue and eigenvector problem but not the 2^N\times 2^N one as for an arbitrary system consisting of N spins 1/2. To illustrate the approach we have presented some new results. Namely, the xx dynamic structure factor for the Ising model in transverse field, the density of states for the isotropic chain with random intersite couplings and transverse fields that linearly depend on the surrounding couplings, and the zz dynamic structure factor for the Ising model in random transverse field. The results obtained are hopped to be useful for an interpretation of observable data for one-dimensional spin-1/2 XY substances.

Oleg Derzhko, Taras Krokhmalskii

Dynamic susceptibility of the one-dimensional spin-1/2 transverse Ising model is obtained by using the numerical approach suggested earlier [Ferroelectrics 153, 55 (1996)]. The dependence of the susceptibility frequency shapes on the value of the transverse field at various temperatures is discussed. The way in which the frequency shape rebuilds as the transverse field increases is illustrated.