Monopole scaling dimension using Monte-Carlo simulation

We present a practical Monte Carlo determination of the scaling dimensions Delta(Q) of flux Q Abelian monopoles through finite-size scaling analysis of the free energy to introduce the background field of classical Dirac monopole-antimonopole pair at critical points of three-dimensional lattice theories. We validate the method in free fermion theory, and by verifying the particle-vortex duality between the monopole scaling dimension at the inverse-XY fixed point and the charge scaling dimension at the XY fixed point. At the O(2) Wilson-Fisher fixed point of the XY model, we determine the critical exponents Delta(1) = 0.13(2), Delta(2) = 0.29(1) and Delta(3) = 0.47(2), which we find to be proportional to the finite-size critical spectrum of monopoles on square torus.