Critical behaviour of compressible Ising models at marginal dimensionalities

M. Vallade , J. Lajzerowicz

Renormalization group methods are applied to study the critical behaviour of a compressible n-component Ising model with short range interactions at d = 4 and a one component Ising model with dipolar interactions at d = 3. The recursion equations are exactly solved in the case of an elastic system of spherical symmetry (d = 4) or cylindrical symmetry (d = 3); new types of logarithmic corrections, corresponding to a Fisher renormalization at marginal dimensions, are found. It is shown that the system exhibits a first-order transition for constant pressure external conditions or when anisotropy is taken into account. The relevance of the calculations to the critical behaviour of uniaxial ferroelectrics is discussed.

Mots clés: ferroelectric transitions; Ising model

Domaines: Articles anciens

M. Vallade, J. Lajzerowicz. Critical behaviour of compressible Ising models at marginal dimensionalities. Journal de Physique, 1979, 40 (6), pp.589-595. ⟨10.1051/jphys:01979004006058900⟩. ⟨jpa-00209143⟩