Variational approach to Hamiltonian lattice theories

A variational calculation of the vacuum energy of a Hamiltonian lattice theory is formulated in terms of a finite box Hamiltonian for a cluster of points. The box Hamiltonian contains surface terms which are proportional to order parameters of the system. It is tested on the Ising model and applied to $Z\left(N\right)\mathrm{}$ spin models in 1 + 1 and 2 + 1 dimensions. $Z\left(3\right)\mathrm{}$ is found to have an exceptional phase-transition structure. The application of the method to local gauge theories is discussed.