First order phase transition with the functional renormalization group method

The renormalization group method, more specifically the Wegner-Houghton equation, is used to find first order phase transitions in a simple scalar field theory with a polynomial potential. An improved definition of the running parameters allows us to explore the renormalization group flow down to the IR endpoint and to locate phase transitions. Beyond the expected first order transition further radiative correction generated first and second order transitions are found. The phase diagram is reviewed by a Monte-Carlo simulation of the lattice regulated version of the theory but the serious slow down of the convergence prevents us from obtaining conclusive results from the simulation.