Abstract
The method of correlated basis functions is applied at the variational level to the Ising model consisting of Pauli spins arranged on a simple cubic lattice, experiencing nearest-neighbor interactions through their $x$ components and subject to a transverse field in the $z$ direction of strength $\ensuremath{\lambda}$. Full optimization of a Hartree-Jastrow trial wave function is performed by solving two Euler-Lagrange equations: a renormalized Hartree equation for the order parameter characterizing the ferromagnetic phase and a paired-magnon equation for the optimal two-spin spatial distribution function. The optimized trial wave function yields a second-order transition with a numerically determined critical coupling of ${\ensuremath{\lambda}}_{c}=5.10$. Explicit results are presented for (i) the magnetization order parameter, (ii) the energy per spin and its potential component, (iii) the static structure function at zero wave number, (iv) the spin-exchange strength, and (v) the magnon energy gap corresponding to a Feynman description of the elementary excitations.
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