An Analytical Study of the O( N ) Nonlinear σ Models on Lattice

Abstract

In the variational cumulant expansion approach, we calculate the internal energy for the d-dhnensional O(N) nonlinear a models on lattice. Specially, we give the results for two-dimensional 0(3), 0(4) and 0(5) models. A comparison with Monte-Carlo (MC) data is also presented. Our formalism can given the results for O(N) nonlinear er models (for any N and any dimensionality d) straightforwardly.