Random Z(2) Higgs Lattice Gauge Theory in Three Dimensions and its Phase Structure
Abstract
We study the threedimensional 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 CoulombHiggs transition diminishes as $p$ increases, and (ii) the firstorder 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 eprints
 Pub Date:
 February 2009
 arXiv:
 arXiv:0902.0142
 Bibcode:
 2009arXiv0902.0142D
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 18 pages, 10 figures