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In this paper we study U(1I2 Hamiltonian lattice gauge theory as a model application of a guidedrandom-walk algorithm. We numerically evaluate the mean plaquette, vacuum energy per plaquette, and plaquette-plaquette correlation functions using the algorithm. The correlation-function measurements indicate that adjacent plaquette phases are weakly anticorrelated in the vacuum state. To our knowledge this is the first measurement of interplaquette correlations using a stochastic Hamiltonian method. We find that our numerical measurements are generally in good agreement with the results of U(lI2 weak-and strong-coupling expansions in the appropriate limits.

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