Strong-coupling expansions for truncated HamiltonianO(n)-spin systems

Abstract

The Hamiltonian formulation of lattice spin systems is used to study the critical properties of a truncated quantum $O\left(n\right)\mathrm{}$-spin model in one and $d$ spatial dimensions for arbitrary $n$. Strong-coupling expansions for the mass gap, ground-state energy density, and susceptibility have been computed up to 14th order and used to search for phase transitions. For $n=0\mathrm{}$ we obtain the exponents for the self-avoiding random-walk problem. In the $O\left(2\right)\mathrm{}$ case we find that the correlation length diverges with an essential singularity at the critical point in 1 + 1 dimensions. No phase transition is found for the $O\left(3\right)\mathrm{}$ and $O\left(4\right)\mathrm{}$ models in the same dimension. Exponents for other values of $n$ are presented and higher dimensions are considered.