**81**, 37-48 (2011)

https://doi.org/10.1140/epjb/e2011-10817-7

## A frustrated quantum spin-s model on the Union Jack lattice with spins s > 1/2

School of Physics and Astronomy, The University of Manchester, Schuster Building, Manchester, M13 9PL, UK

Corresponding author: ^{a}
peggyhyli@googlemail.com

Received:
25
October
2010

Revised:
31
January
2011

Published online:
8
April
2011

The zero-temperature phase diagrams of a two-dimensional (2D) frustrated quantum antiferromagnetic system, namely the Union Jack model, are studied using the coupled cluster method (CCM) for the two cases when the lattice spins have spin quantum number *s* = 1 and *s* = . The system is defined on a square lattice and the spins interact via isotropic Heisenberg interactions such that
all nearest-neighbour (NN) exchange bonds are present with identical
strength *J*_{1} > 0, and only half of the next-nearest-neighbour (NNN) exchange bonds are present with identical strength *J*_{2} *≡* *κ* *J*_{1} > 0. The bonds are arranged such that on the 2×2 unit cell they form the pattern of the Union Jack
flag. Clearly, the NN bonds by themselves (viz., with *J*_{2} = 0)
produce an antiferromagnetic Néel-ordered phase, but as the
relative strength *κ* of the frustrating NNN bonds is increased
a phase transition occurs in the classical case (*s* → *∞*) at *κ*_{c}^{cl} = 0.5 to a canted ferrimagnetic
phase. In the quantum cases considered here we also find strong
evidence for a corresponding phase transition between a
Néel-ordered phase and a quantum canted ferrimagnetic phase at a
critical coupling *κ*_{c1} = 0.580 *±* 0.015 for *s* = 1 and
*κ*_{c1} = 0.545 *±* 0.015 for *s* = . In both cases
the ground-state energy *E* and its first derivative *dE*/*dκ*
seem continuous, thus providing a typical scenario of a second-order
phase transition at *κ* = *κ*_{c1}. However, the order
parameter for the transition (viz., the average ground-state on-site
magnetization) does not go to zero there on either side of the
transition. Thus, the phase transition at *κ* = *κ*_{c1} between the Néel antiferromagnetic phase and the canted ferrimagnetic phase for both the *s* = 1 and *s* = Union Jack models is similar in nature to that found previously for the *s* = Union Jack model. It is thus also completely
comparable to the transition in the *s* = *XXZ* model on the
2D square lattice between two Néel antiferromagnetic phases, one aligned along the *z*-axis and the other along some perpendicular direction in the *xy*-plane.

*© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2011*