The Blume–Capel model on hierarchical lattices: Exact local properties

Mário J.G. Rocha-Neto, G. Camelo-Neto, E. Nogueira and S. Coutinho

Physica A: Statistical Mechanics and its Applications, 2018, vol. 494, issue C, 559-573

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.

Keywords: Blume–Capel model; Spin one Ising model; Hierarchical lattices; Local magnetization; Ordered paramagnetic phase; Multifractal local properties (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:494:y:2018:i:c:p:559-573

DOI: 10.1016/j.physa.2017.11.156

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