The transverse Ising model by CBF

The method of correlated basis functions (CBF) is applied at the variationa l level to the transverse Ising model in two and three spatial dimensions ( D = 2, 3). The model consists of Pauli spins arranged on a simple square or cubic lattice, experiencing nearest-neighbor interactions through their x components and subject to a transverse field in the 2 direction of strength lambda. Working at zero temperature, full optimization of a Hartree-Jastro w trial wave function is performed by solving two Euler-Lagrange equations, namely a renormalized Hartree equation for the order parameter characteriz ing the ferromagnetic phase and a paired-magnon equation for the optimal tw o-spin spatial distribution function. The optimized trial wave function yie lds a second-order transition with a numerically determined critical coupli ng of lambda(c) = 3.14 (D = 2) or lambda(c) = 5.10 (D = 3). Numerical resul ts have been obtained for the magnetization order parameter, the energy per spin and its potential component, the static structure function at zero wa ve number, and the magnon energy gap corresponding to a Feynman description of the elementary excitations. Correlated density matrix theory provides f or a natural extension of this approach to finite temperature.