Renormalization group analysis of Blume-Capel ferromagnet on two-dimensional triangular lattice

• Published in: Physica scripta Vol. 90; no. 8; pp. 85206 - 7
• Main Author: Najafi, M N
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.08.2015
• Subjects: Asymptotic properties; Blume-Capel model; Critical point; Eigenvalues; Ferromagnetism; Lattices; Mathematical models; phase diagram; Phase diagrams; Phase transformations; renormalization group
• ISSN: 0031-8949; 1402-4896
• DOI: 10.1088/0031-8949/90/8/085206

The Blume-Caple model on the triangular lattice is considered in this paper. Using the (perturbative) real-space renormalization group (RSRG) technique we analytically obtain the running of the parameters of the model, i.e., the exchange integral J and the crystal field Δ. The observations show that the first-order calculations are insufficient to capture the tricritical phenomena, and the RG analysis based on second-order expansion of the partition function show qualitative agreement with the previous works. This reveals that the second-order perturbation works appropriately, to obtain the qualitative features of the phase diagram of the model, e.g., a tricritical point which is unstable towards the Ising critical point from one side (which forms the line of second order, separating the ferromagnetic and paramagnetic phases) and the critical point at and from the other side (which forms the line of first-order transition separating ferromagnetic and zero state phases). This analysis shows also that there is another unstable critical point at , with the RG eigenvalue in the Δ-direction (towards S = 0 zero state and paramagnetic phases).