Low-temperature expansion in the d = 4 Ising model

Charles James Elliot

Rodrigo Bissacot, Henrique Corsini

M F Sykes, David S. Gaunt

The derivation of low temperature (high field) expansions for the Ising model with spin S > 4 is described.

Lawrence E. Thomas, Yin Zhong

By conditioning on a subalgebra of observables, we develop low temperature expansions for certain quantum Ising models, which include transverse Ising models and anisotropic xy models. These expansions are majorized by the series for functions solving certain nonlinear partial differential equations. Convergence for the majorizing series follows from Cauchy–Kowalevski theory applied to the partial differential equations. The low temperature expansions imply long-range order.

H. Arisue, Kanehito Tabata

Andrea Pelissetto C, Ettore Vicari

We study the low-temperature effective potential of the Ising model. We evaluate the three-point and four-point zero-momentum renormalized coupling constants that parametrize the expansion of the effective potential near the coexistence curve. These results are obtained by a constrained analysis of the ǫ-expansion that uses accurate estimates for the two-dimensional Ising model.