Convergence of the Linear Delta Expansion in the Critical O(N) Field Theory

The linear delta expansion is applied to the 3-dimensional O(N) scalar field theory at its critical point in a way that is compatible with the large-N limit. For a range of the arbitrary mass parameter, the linear delta expansion for converges, with errors decreasing like a power of the order n in delta. If the principal of minimal sensitivity is used to optimize the convergence rate, the errors seem to decrease exponentially with n.Comment: 26 pages, latex, 8 figure

On the Convergence of the Linear Delta Expansion for the Shift in T_c for Bose-Einstein Condensation

The leading correction from interactions to the transition temperature T_c for Bose-Einstein condensation can be obtained from a nonperturbative calculation in the critical O(N) scalar field theory in 3 dimensions with N=2. We show that the linear delta expansion can be applied to this problem in such a way that in the large-N limit it converges to the exact analytic result. If the principal of minimal sensitivity is used to optimize the convergence rate, the errors seem to decrease exponentially with the order in the delta expansion. For N=2, we calculate the shift in T_c to fourth order in delta. The results are consistent with slow convergence to the results of recent lattice Monte Carlo calculations.Comment: 26 pages, latex, 8 figure