Random Z(2) Higgs Lattice Gauge Theory in Three Dimensions and its Phase Structure

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We study the three-dimensional random Z(2) lattice gauge theory with Higgs field, which has the link Higgs coupling c₁ SUS and the plaquette gauge coupling c₂ UUUU. The randomness is introduced by replacing c₁ → -c₁ for each link with the probability p₁ and c₂ → -c₂ for each plaquette with the probability p₂. We calculate the phase diagram by a new kind of mean field theory that does not assume the replica symmetry and also by Monte Carlo simulations. For the case p₁=p₂(≡ p), the Monte Carlo simulations exhibit that (i) the region of the Higgs phase in the Coulomb-Higgs transition diminishes as p increases, and (ii) the first-order phase transition between the Higgs and the confinement phases disappear for p ≥ pc ≃ 0.01. We discuss the implications of the results to the quantum memory studied by Kitaev et al. and the Z(2) gauge neural network on a lattice.