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 σ/m 2 determined for the φ 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. *

String effects in the Wilson loop: a high precision numerical test

“…This is the case for instance of the ratio between the critical temperature and the square root of the string tension, or the behavior of the spatial string tension above the deconfinement transition. Recently this same universality has been evidentiated in the pattern of the glueball states for various three dimensional gauge models [16]. All these examples show a substantial independence on the gauge group and a small and smooth dependence on the number of spacetime dimensions.…”

Spectrum of the gauge Ising model in three dimensions

“…Looking at tab.1 we see that the biggest discrepancy in the mass values is for the lowest state, which is predicted to be too light in the IP model, and turns out to be very different in the Ising and SU (2) cases. This is due first to the lack of validity of the adiabatic approximation at small scales and second to the fact that in the IP model an "ideal" picture of string (without self repulsion terms) is assumed for the flux tube.…”

Bound states and glueballs in three-dimensional Ising systems

“…5 contains the Monte Carlo results for the glueball masses (from Ref. [17]), normalized to the mass of the lowest glueball. This shows that our dual bound state picture indeed explains the peculiar qualitative features of the glueball spectrum.…”

“…It is very likely that § The 2 + state could be realized with n c = 2, but a general theorem (see Ref. [17]) forces all states with J = 0 to be degenerate in parity. the degeneracies actually group together larger and larger sets of states as the number of constituents is increased.…”