The renormalized thermal mass and critical temperature of a complex scalarfield theory with non-zero charge density

The linear delta expansion is used to obtain the self-energy up to O(delta (2)) For a complex scalar field theory with a lambda(phi*phi)(2) interactio n at high temperature and non-zero chemical potential mu. The calculation i s performed in the imaginary-time formalism via the Hamiltonian form of the path integral and non-perturbative results are generated by a systematic o rder by order variational procedure. The behaviour of the renormalized mass as a function of T and mu is found and the critical temperature extracted This is plotted as a function of mu and compared with the result of resumme d perturbation theory. A detailed calculation of the high-temperature limit of the two-loop "setting-sun" diagram is given, which can easily be adapte d to standard perturbation theory. (C) 2001 Elsevier Science B.V. All right s reserved.