Phase Transitions in Spin-One Ising and Classical Planar Models: Series Studies.

Phase transitions of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on several decorated planar lattices consisting of interconnected diamonds are investigated within the framework of the generalized decoration-iteration transformation. The main attention is paid to the systematic study of the finite-temperature phase diagrams in dependence on the lattice topology. The critical behaviour of the hybrid quantum-classical Ising-Heisenberg model is compared with the relevant behaviour of its semi-classical Ising analogue. It is shown that both models on diamond-like decorated planar lattices exhibit a striking critical behaviour including reentrant phase transitions. The higher the lattice coordination number is, the more pronounced reentrance may be detected.Phase transitions of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on several decorated planar lattices consisting of interconnected diamonds are investigated within the framework of the generalized decoration-iteration transformation. The main attention is paid to the systematic study of the finite-temperature phase diagrams in dependence on the lattice topology. The critical behaviour of the hybrid quantum-classical Ising-Heisenberg model is compared with the relevant behaviour of its semi-classical Ising analogue. It is shown that both models on diamond-like decorated planar lattices exhibit a striking critical behaviour including reentrant phase transitions. The higher the lattice coordination number is, the more pronounced reentrance may be detected.

arXiv:1106.4687Condensed Matter PhysicsJan 1, 201113 citations

First-order phase transitions in spin-one Ising systems

Robert B. Griffiths

PhysicaJan 1, 196793 citations

Phase transitions in the classical n -vector model on the fcc lattice

J. Ricardo de Sousa, J. A. Plascak

The classical $n$ -vector model on the face-centered cubic lattice with ferromagnetic and antiferromagnetic interactions is studied by using the framework of an effective field theory approach in cluster with two spins. For $n=1$ (Ising), $n=2$ ( $XY$ -planar rotator), $n=3$ (Heisenberg), and $n\ensuremath{\rightarrow}\ensuremath{\infty}$ (spherical) models the ferromagnetic system undergoes a second-order phase transition while the antiferromagnetic system presents a first-order behavior. The first-order character for $n=3$ , which is inconclusive in the literature, seems actually to be the case for the isotropic Heisenberg antiferromagnet, and the same is expected to hold for the less studied $XY$ and spherical models. In addition, the transition temperatures are quantitatively comparable to the exact one (when available) and to those from Monte Carlo simulations and series expansion.The classical $n$-vector model on the face-centered cubic lattice with ferromagnetic and antiferromagnetic interactions is studied by using the framework of an effective field theory approach in cluster with two spins. For $n=1$ (Ising), $n=2$ ($XY$-planar rotator), $n=3$ (Heisenberg), and $n\ensuremath{\rightarrow}\ensuremath{\infty}$ (spherical) models the ferromagnetic system undergoes a second-order phase transition while the antiferromagnetic system presents a first-order behavior. The first-order character for $n=3$, which is inconclusive in the literature, seems actually to be the case for the isotropic Heisenberg antiferromagnet, and the same is expected to hold for the less studied $XY$ and spherical models. In addition, the transition temperatures are quantitatively comparable to the exact one (when available) and to those from Monte Carlo simulations and series expansion.

Physical Review BJan 18, 20086 citations

Phase Diagram of a Spin-One Ising System

Fengcheng Wu

Chinese Journal of PhysicsApr 1, 19789 citations

The classical

n

-vector model on the face-centered cubic lattice with ferromagnetic and antiferromagnetic interactions is studied by using the framework of an effective field theory approach in cluster with two spins. For

n=1

(Ising),

n=2

(

XY

-planar rotator),

n=3

(Heisenberg), and $n\ensuremath{\rightarrow}\ensuremath{\infty}$ (spherical) models the ferromagnetic system undergoes a second-order phase transition while the antiferromagnetic system presents a first-order behavior. The first-order character for

n=3

, which is inconclusive in the literature, seems actually to be the case for the isotropic Heisenberg antiferromagnet, and the same is expected to hold for the less studied

XY

and spherical models. In addition, the transition temperatures are quantitatively comparable to the exact one (when available) and to those from Monte Carlo simulations and series expansion.