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Hamiltonian calculations for the Z 2 lattice gauge theory with matter fields

1981; American Physical Society; Volume: 23; Issue: 12 Linguagem: Inglês

10.1103/physrevd.23.2962

1538-4500

Jay L. Banks, D.K. Sinclair,

High-Energy Particle Collisions Research

We study the ${Z}_{2}$ lattice gauge theory coupled to scalar matter fields (Ising spins) in 2 + 1 dimensions. Strong-coupling expansions are obtained for the masses of both "meson" and "glueball" excitations. We use the zeros of the mass gap, obtained using Pad\'e approximants and duality transformations, to locate second-order phase transitions as a function of the gauge and matter coupling constants. The resulting phase diagram is in reasonable agreement with that obtained by other methods. These other methods (Monte Carlo and $\frac{1}{N}$ expansions) are, however, most sensitive to first-order phase transitions while our method is most sensitive to continuous phase transitions. We observe that the additional parameter of the Hamiltonian approach is essentially irrelevant.