Random Z(2) Higgs Lattice Gauge Theory in Three Dimensions and its Phase Structure
Abstract
We study the three-dimensional random Z(2) lattice gauge theory with Higgs field, which has the link Higgs coupling $c_1 SUS$ and the plaquette gauge coupling $c_2 UUUU$. The randomness is introduced by replacing $c_1 \to -c_1$ for each link with the probability $p_1$ and $c_2 \to -c_2$ for each plaquette with the probability $p_2$. 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 $p_1=p_2(\equiv p)$, 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 $p \ge p_c \simeq 0.01$. 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2009
- DOI:
- 10.48550/arXiv.0902.0142
- arXiv:
- arXiv:0902.0142
- Bibcode:
- 2009arXiv0902.0142D
- Keywords:
-
- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Disordered Systems and Neural Networks
- E-Print:
- 18 pages, 10 figures