We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum -- and, in particular, classical -- interactions. Our approach is based on the use of ``decoupling parameters", advocated by Park [34], which relates partition functions with successive additional interaction terms. Our treatment, however, leads to an explicit expansion in a
β-dependent effective fugacity that permits an explicit evaluation of free energy and correlation functions at small
β. To determine its convergence region we adopt a relatively recent cluster summation scheme that replaces the traditional use of Kikwood-Salzburg-like integral equations by more precise sums in terms of particular tree-diagrams [2]. As an application we show that our lower bound of the radius of
β-analyticity is larger than Park's for quantum systems two-body interactions.
The Wick reduction theorem is used in a linked-cluster-expansion calculation to facilitate the evaluation of the multi-integrals of the ordered products encountered in the expansion. The method resolves a major problem in the general linked-cluster expansion for quantum spin systems. We apply it to the evaluation of the perpendicular susceptibility of the Ising model. An eighth-order linked-cluster series is obtained for a general lattice. The temperature behavior of the perpendicular susceptibility of the three-dimensional Ising model (fcc lattice) is discussed.
We calculate thermodynamic properties of soft-core lattice bosons with on-site
n-body interactions using up to twelfth- and tenth-order strong coupling expansion in one- and two-dimensional cubic lattices at zero temperature. Using linked cluster techniques, we show that it is possible to exactly renormalize the two-body interactions for quasiparticle excitations and ground-state energy by resumming the three- and four-body terms in the system, which suggests that all higher-body on-site interactions may be exactly and perturbatively resummed into the two-body terms for similar system observables. The renormalization procedure that we develop is applicable to a broad range of systems analyzable by linked cluster expansions, ranging from perturbative quantum chromodynamics to spin models, giving either an exact or approximate resummation depending on the specific system and properties. Universality at various three-body interaction strengths for the two-dimensional boson Hubbard model is checked numerically.