Blume–Capel Model in D=1 With Long-Range Interactions: Giant Reentrance in the Finite-Temperature Tricritical Phase Diagrams

Abstract

The Blume–Capel model in one dimension with long-range power-law interactions is studied by renormalization-group theory. A series of finite-temperature tricritical phase diagrams is found, as a function of the power-law exponent of the power-law interactions. These calculated phase diagrams exhibit a giant reentrance in the form disorder-order–disorder as temperature is lowered. The first-order transition takes over the entire phase boundary at longest-range interactions, as a near-equivalent-neighbor regime is approached. © 2026 Elsevier B.V.