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We introduce a lattice model with local U(1) gauge symmetry which incorporates explicit frustration in d > 2. The form of the action is inspired from the loop expansion of the fermionic determinant in standard lattice QED. We study through numerical simulations the phase diagram of the model, revealing the existence of a frustrated (antiferromagnetic) phase for d = 3 and d = 4, once an appropriate order parameter is identified. [ABSTRACT FROM AUTHOR]

Motivated by the sign problem in several systems, we have developed a geometric simulation algorithm based on the strong coupling expansion which can be applied to abelian pure gauge models. We have studied the algorithm in the U(1) model in 3 and 4 dimensions, and seen that it is practical and is similarly efficient to the standard heat-bath algorithm, but without the ergodicity problems which comes from the presence of vortices. We have also applied the algorithm to the Ising gauge model at the critical point, and we find hints of a better asymptotic behaviour of the autocorrelation time, which therefore suggests the possibility of a smaller dynamical critical exponent with respect to the standard heat-bath algorithm. [ABSTRACT FROM AUTHOR]