Spectrum of the gauge Ising model in three dimensions

Abstract

We present a high precision Monte Carlo study of the spectrum of the Z2 gauge theory in three dimensions in the confining 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 SU(2) spectrum and with the prediction of the Isgur-Paton model. Our data strongly support the conjecture that the glueball spectrum is described by some type of flux tube model. We also compare the spectrum with some recent results for the correlation length in the 3d spin Ising model. This analysis sheds light on some nontrivial features of the duality transformation.

The glue-ball spectrum of pure percolation

“…The universal ratio m 0 + 0 √ σ ≃ 4.46 is then evaluated. Its value is surprisingly close to the ≃ 4.7 reported for SU (2) in the same dimensionality in [4] and refined in [5], and of the same order of magnitude as the amplitude obtained for the Ising model. This fact confirms that the essential mechanism responsible for confinement is well included in the simpler percolation model.…”

“…Our basis was made by the following 17 loops (called tetrises for short) 3 : , , , , , , , , , , , , , , The same process can be applied to the other spin/parity channels; in these cases, however, one has to choose loop shapes not completely invariant under dihedral symmetry, and then construct proper linear combinations of the differently oriented copies of them. This approach has been successfully applied to the 3D Ising model spectrum in [2]. Example of observables constructed this way are:…”

“…Following this prescription, we constructed, for each non-0 + channel, a basis of operators by making use of the following tetrises: For a given channel J P , by diagonalising the cross-correlation matrices C (J P ) i j (t) one can identify (effective) masses in the spin/parity family: this can be achieved with a naive diagonalisation for each value of t, or with a generalised eigenvalue problem (see, for instance, [2]) by fixing a suitable t 0 in:…”

“…We refer to that paper, and references therein, for a more detailed discussion on this introductory subject 2. What is described here is the so-called bond percolation, but the situation is the same for the site percolation, apart from some implementation nuisances.…”