CORRELATED-BASIS-FUNCTION ANALYSIS OF THE TRANSVERSE ISING-MODEL

Correlated-basis-function (CBF) theory, which has provided a firm foun dation for ab initio calculations of the properties of quantum fluids such as liquid He-4, is adapted and applied at the Jastrow-Feenberg va riational level to give an optimized description of the structure and of the elementary excitations of the Ising-spin model in a transverse magnetic field. A set of trial wave functions of Hartree-Jastrow form is assumed to describe the spatial correlations present in the ordered as well as the disordered ground states, and the Feynman Ansatz is co nsistently adopted to represent the elementary magnon states. The CBF analysis of the spin system employs the hypernetted-chain (HNC) formal ism for a substitutional binary mixture of bosons and derives HNC equa tions for the spatial distribution functions which determine the groun d-state energy expectation value. Functional variation of this quantit y with respect to the magnetic order parameter and the trial states le ads to two Euler-Lagrange equations, which may be interpreted as a ren ormalized Hartree equation for the optimal magnetization and as a pair ed-magnon equation for the magnetic correlation function that is analo gous to the familiar paired-phonon equation for conventional quantum f luids. Numerical calculations are based on simple cubic lattices and a n optimized nearest-neighbor Ansatz for the generating pseudopotential . Results are reported on the order parameter, the energy per lattice site, the transverse magnetization, and the magnon excitation energies as functions of the coupling parameter 0 less than or equal to lambda less than or equal to infinity measuring the strength of the transver se magnetic field. We also present numerical results on the magnetic c orrelation function, the static structure function, and the correlatio n length. The system exhibits a second-order phase transition at a cri tical value lambda(c) of the coupling strength. Our numerical calculat ions of the optimal order parameter yields lambda(c) similar or equal to 5.17 for a simple cubic lattice and lambda(c) similar or equal to 3 .12 for a square planar lattice. The calculated data are in very good agreement with results derived from perturbation expansions in conjunc tion with Pade techniques.