Application of the linked cluster expansion to the n-component φ4 theory

The linked cluster (high-temperature) expansion is worked out through 14th order for the O(n) symmetric φ4 theory on a d-dimensional simple hypercubic lattice. The quantities expanded are the renormalized mass mR, the wave-function renormalization constant ZR and the renormalized coupling gR at zero momentum. The results obtained apply for all n and bare couplings, and for d=2, 3, 4. Because a huge number of irreducible graphs (about 100 000) contribute to the order considered, a fully computerized approach was necessary, which we describe here in some detail. The series will be applied elsewhere to solve the 4-component model on a four-dimensional lattice. (orig.)