Exact Renormalization Group Exhibiting a Tricritical Fixed Point for a Spin-1 Ising Model in One Dimension

Abstract

Exact renormalization-group recursion relations are studied for a spin-1 Ising model in one dimension. In this model, critical lines are marked by a double degeneracy of the largest eigenvalue of the transfer matrix, and the tricritical point by a triple degeneracy. This is directly related to the tricritical fixed point being more unstable than the critical fixed points.

Exactly solved mixed spin-(1,1/2) Ising–Heisenberg diamond chain with a single-ion anisotropy

“…(5) one readily gets a rigorous mapping relation between the partition function  of the mixed spin-(1,1/2) Ising-Heisenberg diamond chain and, respectively, the partition function  BEG of the generalized spin-1 Blume-Emery-Griffiths (BEG) chain [38][39][40] with the effective bilinear interaction R, the single-ion anisotropy D 0 , the biquadratic interaction Q, the two-spin third-order interaction L, and the magnetic field h 0…”

Exactly solvable spin-1 Ising–Heisenberg diamond chain with the second-neighbor interaction between nodal spins

“…[23,24,25]. Of course, individual elements of the transfer matrix (5) are defined through the formula…”

“…(4), the partition function of the spin-1 Ising-Heisenberg diamond chain can be expressed through three eigenvalues of the transfer matrix [23,24] …”

Magnetization plateaus of an exactly solvable spin-1 Ising–Heisenberg diamond chain

“…[21,22,23]. Of course, individual elements of the transfer matrix (5) are defined through the formula…”

“…(4), the partition function of the spin-1 Ising-Heisenberg diamond chain can be expressed through three eigenvalues of the transfer matrix (5) explicitly given in Refs. [21,22,23]…”