The Blume-Capel Model on Hierarchical Lattices: exact local properties

TL;DR

This paper investigates the local properties of the spin one ferromagnetic Blume-Capel model on hierarchical lattices, revealing phase transitions, multifractal magnetization profiles, and potential tricritical points through numerical recursion.

Contribution

It provides an exact numerical analysis of local properties and phase transitions in the Blume-Capel model on hierarchical lattices, including multifractal magnetization profiles.

Findings

Discontinuous phase transitions from ferromagnetic to ordered paramagnetic phases.

Broad multifractal spectrum of magnetization profiles at transition lines.

Identification of low-temperature region where tricritical points may occur.

Abstract

The local properties of the spin one ferromagnetic Blume-Capel model defined on hierarchical lattices with dimension two and three are obtained by a numerical recursion procedure and studied as functions of the temperature and the reduced crystal-field parameter. The magnetization and the density of sites in the configuration S=0 state are carefully investigated at low temperature in the region of the phase diagram that presents the phenomenon of phase reentrance. Both order parameters undergo transitions from the ferromagnetic to the ordered paramagnetic phase with abrupt discontinuities that decrease along the phase boundary at low temperatures. The distribution of magnetization in a typical profile was determined on the transition line presenting a broad multifractal spectrum that narrows towards the fractal limit (single point) as the discontinuities of the order parameters grow towards a maximum. The amplitude of the order-parameter discontinuities and the narrowing of the multifractal spectra were used to delimit the low temperature interval for the possible locus of the tricritical point.