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

Abstract

The spin-3 2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d = 3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d = 3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.

Blume-Capel ferromagnet driven by propagating and standing magnetic field wave: Dynamical modes and nonequilibrium phase transition

“…The critical behaviours of S = 3 2 was studied [7]. It should be mentioned here that the variety of positional and/or orientational order and a very rich phase diagram was obtained [8] recently even in S = 3 2 Ising system in three dimensions by renormalization group theory in Migdal-Kadanoff approximation. The general spin BC model was studied [9] by meanfield approximation.…”

Devil's staircase continuum in the chiral clock spin glass with competing ferromagnetic-antiferromagnetic and left-right chiral interactions

“…On the other hand, this approximation for the cubic lattice is an uncontrolled approximation, as in fact are all renormalization-group theory calculations in d = 3 and all mean-field theory calculations. However, as noted before [40], the local summation in position-space technique used here has been qualitatively, near quantitatively, and predictively successful in a large variety of problems, such as arbitrary spin-s Ising models [41], global Blume-Emery-Griffiths model [42], first-and second-order Potts transitions [43,44], antiferromagnetic Potts critical phases [9,10], ordering [45] and superfluidity [46] on surfaces, multiply re-entrant liquid crystal phases [47,48], chaotic spin glasses [49], randomfield [50,51] and random-temperature [52,53] magnets including the remarkably small d = 3 magnetization critical exponent β of the random-field Ising model, and hightemperature superconductors [54].…”

Chiral Potts spin glass ind=2and 3 dimensions

“…This approximation for the cubic lattice is an uncontrolled approximation, as in fact are all renormalization-group theory calculations in d = 3 and all mean-field theory calculations. However, as noted before [45], the local summation in position-space technique used here has been qualitatively, near-quantitatively, and predictively successful in a large variety of problems, such as arbitrary spin-s Ising models [46], global BlumeEmery-Griffiths model [47], first-and second-order Potts transitions [48,49], antiferromagnetic Potts critical phases [50,51], ordering [6] and superfluidity [52] on surfaces, multiply reentrant liquid crystal phases [53,54], chaotic spin glasses [55], random-field [56,57] and random-temperature [58,59] magnets, including the remarkably small d = 3 magnetization critical exponent β of the random-field Ising model, and high-temperature superconductors [60]. Thus, this renormalization-group approximation continues to be widely used [61][62][63][64][65][66][67][68][69][70][71][72][73][74].…”