Nuclear Physics B161 (1979) 533.-547 0 North-Holland Publishing Company RENORMALIZATION GROUP CALCULATION FOR Z(2) GAUGE THEORY l D. HORN and S. YANKIELOWICZ Department of Physics ard Astronomy, Tel Aviv University, Ramat Aviv, Israel Received 23 July 1979 (Revised 5 September 1979) A renormalization group block-spin scheme for Z(2) gauge theory is constructed using a hamiltonian formulation. The renormalization group equations enable us to cal- culate the critical coupling and critical exponents both in 2 + 1 and 3 + 1 dimensions. The results compare favorably with those of the Ising model in a transverse field in the 2 + 1 case. In 3 + 1 dimensions the results turn out to satisfy the selfduality constraint. The critical exponents obtained are in agreement with the Migdal conjecture. 1. Introduction Z(N) gauge theories are the most simple systems which possess local gauge sym- metry. The physical interest in these models is quite large, ranging from the confine- ment problem to spin glass [ 1,2]. The calculation schemes that were used up to now were based on perturbation theory (for small as well as for large coupling constants) and Pad6 approximations [ 1,2]. In this paper we would like to present a renorma- lization group block-spin calculation which is non-perturbative and allows one to survey the whole range of the coupling constant. The method is constructed and the calculations are carried out within the framework of the Z(2) gauge theory. The basic idea is to perform successive calculations which involve diagonalization of block hamiltonians, truncation and rewriting the new hamiltonian in the truncated Hilbert space. It is an extension of the method described in ref. [3]. The new important element here is the local gauge symmetry which one would like to preserve. It is precisely the gauge conditions at each lattice point which make the block-spinning difficult since they correlate essentially all the plaquettes. In our approach we pre- serve the gauge invariance in an average sense. Unlike the situation in ref. [3] (global symmetry) we have to perform the renormalization in two stages. In the first l Work supported in part by the Israel Commission for Basic Research US-Israel Bi-national Science Foundation (BSF). 533