13 research outputs found
Spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions as the exactly soluble zero-field eight-vertex model
The spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction
and quartic Ising interactions is exactly solved by establishing a precise
mapping relationship with the corresponding zero-field (symmetric) eight-vertex
model. It is shown that the Ising-Heisenberg model with the ferromagnetic
Heisenberg interaction exhibits a striking critical behavior, which manifests
itself through re-entrant phase transitions as well as continuously varying
critical exponents. The changes of critical exponents are in accordance with
the weak universality hypothesis in spite of a peculiar singular behavior to
emerge at a quantum critical point of the infinite order, which occurs at the
isotropic limit of the Heisenberg interaction. On the other hand, the
Ising-Heisenberg model with the antiferromagnetic Heisenberg interaction
surprisingly exhibits less significant changes of both critical temperatures as
well as critical exponents upon varying a strength of the exchange anisotropy
in the Heisenberg interaction.Comment: 11 pages, 9 figure
Exact evidence for the spontaneous antiferromagnetic long-range order in the two-dimensional hybrid model of localized Ising spins and itinerant electrons
The generalized decoration-iteration transformation is adopted to treat
exactly a hybrid model of doubly decorated two-dimensional lattices, which have
localized Ising spins at their nodal lattice sites and itinerant electrons
delocalized over pairs of decorating sites. Under the assumption of a half
filling of each couple of the decorating sites, the investigated model system
exhibits a remarkable spontaneous antiferromagnetic long-range order with an
obvious quantum reduction of the staggered magnetization. It is shown that the
critical temperature of the spontaneously long-range ordered quantum
antiferromagnet displays an outstanding non-monotonic dependence on a ratio
between the kinetic term and the Ising-type exchange interaction.Comment: 8 pages, 6 figure
Phase transitions of the mixed spin-1/2 and spin-S Ising model on a three-dimensional decorated lattice with a layered structure
Phase transitions of the mixed spin-1/2 and spin-S (S >= 1/2) Ising model on
a three-dimensional (3D) decorated lattice with a layered magnetic structure
are investigated within the framework of a precise mapping relationship to the
simple spin-1/2 Ising model on the tetragonal lattice. This mapping
correspondence yields for the layered Ising model of mixed spins plausible
results either by adopting the conjectured solution for the spin-1/2 Ising
model on the orthorhombic lattice [Z.-D. Zhang, Philos. Mag. 87 (2007)
5309-5419] or by performing extensive Monte Carlo simulations for the
corresponding spin-1/2 Ising model on the tetragonal lattice. It is shown that
the critical behaviour markedly depends on a relative strength of axial
zero-field splitting parameter, inter- and intra-layer interactions. The
striking spontaneous order captured to the 'quasi-1D' spin system is found in a
restricted region of interaction parameters, where the zero-field splitting
parameter forces all integer-valued decorating spins towards their
'non-magnetic' spin state.Comment: 18 pages, 5 figures, Monte Carlo simulation data has been added to
this revised versio
Exact results of the mixed-spin Ising model on a decorated square lattice with two different decorating spins of integer magnitudes
The mixed-spin Ising model on a decorated square lattice with two different
decorating spins of the integer magnitudes S_B = 1 and S_C = 2 placed on
horizontal and vertical bonds of the lattice, respectively, is examined within
an exact analytical approach based on the generalized decoration-iteration
mapping transformation. Besides the ground-state analysis, finite-temperature
properties of the system are also investigated in detail. The most interesting
numerical result to emerge from our study relates to a striking critical
behaviour of the spontaneously ordered 'quasi-1D' spin system. It was found
that this quite remarkable spontaneous order arises when one sub-lattice of the
decorating spins (either S_B or S_C) tends towards their 'non-magnetic' spin
state S = 0 and the system becomes disordered only upon further single-ion
anisotropy strengthening. The effect of single-ion anisotropy upon the
temperature dependence of the total and sub-lattice magnetization is also
particularly investigated.Comment: 17 pages, 6 figure
Exact solution of the geometrically frustrated spin-1/2 Ising-Heisenberg model on the triangulated Kagome (triangles-in-triangles) lattice
The geometric frustration of the spin-1/2 Ising-Heisenberg model on the
triangulated Kagome (triangles-in-triangles) lattice is investigated within the
framework of an exact analytical method based on the generalized star-triangle
mapping transformation. Ground-state and finite-temperature phase diagrams are
obtained along with other exact results for the partition function, Helmholtz
free energy, internal energy, entropy, and specific heat, by establishing a
precise mapping relationship to the corresponding spin-1/2 Ising model on the
Kagome lattice. It is shown that the residual entropy of the disordered spin
liquid phase is for the quantum Ising-Heisenberg model significantly lower than
for its semi-classical Ising limit (S_0/N_T k_B = 0.2806 and 0.4752,
respectively), which implies that quantum fluctuations partially lift a
macroscopic degeneracy of the ground-state manifold in the frustrated regime.
The investigated model system has an obvious relevance to a series of polymeric
coordination compounds Cu_9X_2(cpa)_6 (X=F, Cl, Br and cpa=carboxypentonic
acid) for which we made a theoretical prediction about the temperature
dependence of zero-field specific heat.Comment: 13 pages, 7 figures, submitted to Phys. Rev.