The Spectrum of the 2+1 Dimensional Gauge Ising Model

Abstract

We present a high precision Monte Carlo study of the spectrum of the $Z_2$ gauge theory in $2+1$ dimensions in the strong coupling phase. Using state of the art Monte Carlo techniques we are able to accurately determine up to three masses in a single channel. We compare our results with the strong coupling expansion for the lightest mass and with results for the universal ratio $\sigma/m^2$ determined for the $\phi^4$-theory. Finally the whole spectrum is compared with that obtained from the Isgur-Paton flux tube model and the spectrum of the $2+1$ dimensional $SU(2)$ gauge theory. A remarkable agreement between the Ising and SU(2) spectra (except for the lowest mass state) is found.