Generalized ensemble algorithm for U(1) gauge theory

The four dimensional pure compact U(1) gauge theory is known to posses a phase transition (PT) separating a confined phase and a Coulomb one and the determination of the order of PT is of great importance. In the pure compact U(1) gauge theory, however, the determination of the order of PT is very difficult since on large lattices the standard updating algorithms like Metropolis, heat-bath, hybrid Monte Carlo (HMC)[1], fail to generate enough tunneling between metastable states. Many efforts have been done to clarify the order of the PT[2]. In spite of such efforts the order of the PT is still controversial. A promising algorithm to overcome this difficulty is the multicanonical algorithm[3] which uses a multicanonical weight in stead of the Boltzmann one and can enhance the tunneling rate between metastable states. Although the multicanonical algorithm works effectively, one disadvantage of the multicanonical algorithm might be that a multicanonical weight used in the simulations is not known a priori and it must be determined before the simulations. Usually the weight is estimated from a short run of the standard updating algorithm. However this estimation is more difficult as a lattice size becomes larger. Recently in several fields where the usual Monte Carlo technique does not work effectively, simulations were performed with the Tsallis weight[4,5], first introduced by Tsallis[6]. The Tsallis weight controlled by a parameter q can be easily defined, and the usual Boltzmann weight is given by taking the limit q → 1. The results have showed that the use of the Tsallis weight might be more advantageous than that of the Boltzmann one. Inspired by such studies, here we apply the Tsallis weight for the hybrid Monte Carlo simulation of the pure compact U(1) lattice gauge theory and investigate whether the Tsallis weight solves the difficulty in determining the order of the PT.