Position-space renormalization-group investigation of the spin-3/2 Blume-Emery-Griffiths model with repulsive biquadratic coupling

Abstract

Phase transitions of a four-component lattice gas or spin-3/2 Blume-Emery-Griffiths model, with a single-ion uniaxial anisotropy and nearest-neighbour pair interactions, both bilinear and biquadratic, are investigated for twodimensional lattices using an approximate renormalization-group approach of the Migdal-Kadanoff type. The set of fixed points and flows provide the characteristic phase diagrams, in the case of repulsive biquadratic interaction, featuring four ordered phases including high-entropy ferrimagnetic and staggered quadrupolar phases. Successive phase transitions and multicritical points are also found.

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of thes=3/2Ising model from renormalization-group theory

“…Thus, we have studied the spin-3 2 Ising model in spatial three dimensions d = 3 with length-rescaling factor b = 3, obtaining the global phase diagram, which is underpinned by 40 renormalizationgroup fixed points (Table I). Similar calculations have been done in d = 2 [7,13] and d = 3 [14].…”

“…Phase diagrams similar to Figs. 1(e) and 1(f) have been seen by renormalization-group theory in d = 2,3 [7,13,14]. The phase diagram sequence in Figs.…”

“…1(e) or around the phase A q in Fig. 1(f), the segments on each side of the points I 13 and I A having different fixed points but same critical exponents (Table I). Phase diagrams similar to Figs.…”

“…Four second-order phase transition lines meet at the tetracritical point N 3 . The inset shows that the phase diagram topology is unaltered near the maximal temperatures of the phase F 13 . In this phase diagram region, as (J 1 − J 3 )/J 13 is further increased, A 3 replaces F 3 , which is Fig.…”

“…The points M 1 and M 3 are tetracritical points. The points I, I 13 , and I A each separate two segments of second-order phase transitions, between the same two phases, where in spite of renormalization-group flows to different basins, critical exponent universality is sustained via redundant fixed points.…”