A solvable twisted one-plaquette model

Abstract

We solve a hot twisted Eguchi-Kawai model with only timelike plaquettes in the deconfined phase, by computing the quadratic quantum fluctuations around the classical vacuum. The solution of the model has some novel features: the eigenvalues of the time-like link variable are separated in L bunches, if L is the number of links of the original lattice in the time direction, and each bunch obeys a Wigner semicircular distribution of eigenvalues. This solution becomes unstable at a critical value of the coupling constant, where it is argued that a condensation of classical solutions takes place. This can be inferred by comparison with the heat-kernel model in the hamiltonian limit, and the related Douglas-Kazakov phase transition in QCD2. As a byproduct of our solution, we can reproduce the dependence of the coupling constant from the parameter describing the asymmetry of the lattice, in agreement with previous results by Karsch.