149 research outputs found
Investigation of phase separation within the generalized Lin-Taylor model for a binary liquid mixture of large hexagonal and small triangular particles
The generalized Lin-Taylor model defined on the hexagonal lattice is used to
investigate the phase separation in an asymmetric binary liquid mixture
consisting of large A (hexagons) and small B (triangles) particles. By
considering interaction energies between A-A and A-B pairs of particles that
occupy nearest-neighbour cells of the hexagonal lattice, we have derived an
exact solution for the considered model system having established a mapping
correspondence with the two-dimensional Ising model on its dual triangular
lattice. Altogether, six different types of coexistence curves including those
with reentrant miscibility regions (i.e. closed-loop coexistence curves) were
found in dependence on the relative strength between both coupling constants.Comment: 8 pages, 4 figures, presented at 7th Liblice conference on the
Statistical Mechanics of Liquids to be held in Lednice on June 11-16, 200
S=1 kagom\'e Ising model with triquadratic interactions, single-ion anisotropy and magnetic field: exact phase diagrams
We consider a S=1 kagom\'e Ising model with triquadratic interactions around
each triangular face of the kagom\'e lattice, single-ion anisotropy and an
applied magnetic field. A mapping establishes an equivalence between the
magnetic canonical partition function of the model and the grand canonical
partition function of a kagom\'e lattice-gas model with localized
three-particle interactions. Since exact phase diagrams are known for
condensation in the one-parameter lattice-gas model, the mapping directly
provides the corresponding exact phase diagrams of the three-parameter S=1
Ising model. As anisotropy competes with interactions, results include the
appearance of confluent singularities effecting changes in the topology of the
phase diagrams, phase boundary curves (magnetic field vs temperature) with
purely positive or negative slopes as well as intermediate cases showing
nonmonotonicity, and coexistence curves (magnetization vs temperature) with
varying shapes and orientations, in some instances entrapping a homogeneous
phase.Comment: 14 pages plus 11 figures; to be published in Physica
Critical Binder cumulant of two-dimensional Ising models
The fourth-order cumulant of the magnetization, the Binder cumulant, is
determined at the phase transition of Ising models on square and triangular
lattices, using Monte Carlo techniques. Its value at criticality depends
sensitively on boundary conditions, details of the clusters used in calculating
the cumulant, and symmetry of the interactions or, here, lattice structure.
Possibilities to identify generic critical cumulants are discussed.Comment: 6 pages, 4 figures, submitted to Eur. Phys. J.
Exact solution of the spin-1/2 Ising model on the Shastry-Sutherland (orthogonal-dimer) lattice
A star-triangle mapping transformation is used to establish an exact
correspondence between the spin-1/2 Ising model on the Shastry-Sutherland
(orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a
bathroom tile (4-8) lattice. Exact results for the critical temperature and
spontaneous magnetization are obtained and compared with corresponding results
on the regular Ising lattices.Comment: 8 pages, 4 figure
On the Critical Temperature of Non-Periodic Ising Models on Hexagonal Lattices
The critical temperature of layered Ising models on triangular and honeycomb
lattices are calculated in simple, explicit form for arbitrary distribution of
the couplings.Comment: to appear in Z. Phys. B., 8 pages plain TEX, 1 figure available upon
reques
Quantum Field Induced Orderings in Fully Frustrated Ising Spin Systems
We study ordering mechanisms which are induced by the quantum fluctuation in
fully frustrated Ising spin systems. Since there are many degenerated states in
frustrated systems, "order by thermal disorder" often takes place due to a kind
of entropy effect. To consider "order by quantum disorder" in fully frustrated
Ising spin systems, we apply transverse field as quantum fluctuation. There
exists a ferromagnetic correlation in each sublattice. The sublattice
correlation at zero temperature is enlarged due to transverse field. The
quantum fluctuation enhances the solid order at zero temperatures. This is an
example of quantum field induced ordering in fully frustrated systems. We also
study a case in which the transverse field induces a reentrant behavior as
another type of order by quantum disorder, and compare correspondent cases in
the classical systems.Comment: 3 pages, 4 figures, submitted to Proceedings of Symposia "Nanoscience
and Quantum Physics
Critical phase of a magnetic hard hexagon model on triangular lattice
We introduce a magnetic hard hexagon model with two-body restrictions for
configurations of hard hexagons and investigate its critical behavior by using
Monte Carlo simulations and a finite size scaling method for discreate values
of activity. It turns out that the restrictions bring about a critical phase
which the usual hard hexagon model does not have. An upper and a lower critical
value of the discrete activity for the critical phase of the newly proposed
model are estimated as 4 and 6, respectively.Comment: 11 pages, 8 Postscript figures, uses revtex.st
The triangular Ising antiferromagnet in a staggered field
We study the equilibrium properties of the nearest-neighbor Ising
antiferromagnet on a triangular lattice in the presence of a staggered field
conjugate to one of the degenerate ground states. Using a mapping of the ground
states of the model without the staggered field to dimer coverings on the dual
lattice, we classify the ground states into sectors specified by the number of
``strings''. We show that the effect of the staggered field is to generate
long-range interactions between strings. In the limiting case of the
antiferromagnetic coupling constant J becoming infinitely large, we prove the
existence of a phase transition in this system and obtain a finite lower bound
for the transition temperature. For finite J, we study the equilibrium
properties of the system using Monte Carlo simulations with three different
dynamics. We find that in all the three cases, equilibration times for low
field values increase rapidly with system size at low temperatures. Due to this
difficulty in equilibrating sufficiently large systems at low temperatures, our
finite-size scaling analysis of the numerical results does not permit a
definite conclusion about the existence of a phase transition for finite values
of J. A surprising feature in the system is the fact that unlike usual glassy
systems, a zero-temperature quench almost always leads to the ground state,
while a slow cooling does not.Comment: 12 pages, 18 figures: To appear in Phys. Rev.
Frustrated spin model as a hard-sphere liquid
We show that one-dimensional topological objects (kinks) are natural degrees
of freedom for an antiferromagnetic Ising model on a triangular lattice. Its
ground states and the coexistence of spin ordering with an extensive
zero-temperature entropy can be easily understood in terms of kinks forming a
hard-sphere liquid. Using this picture we explain effects of quantum spin
dynamics on that frustrated model, which we also study numerically.Comment: 5 pages, 3 figure
Thermally-induced magnetic phases in an Ising spin Kondo lattice model on a kagome lattice at 1/3-filling
Numerical investigation on the thermodynamic properties of an Ising spin
Kondo lattice model on a kagome lattice is reported. By using Monte Carlo
simulation, we investigated the magnetic phases at 1/3-filling. We identified
two successive transitions from high-temperature paramagnetic state to a
Kosterlitz-Thouless-like phase in an intermediate temperature range and to a
partially disordered phase at a lower temperature. The partially disordered
state is characterized by coexistence of antiferromagnetic hexagons and
paramagnetic sites with period . We compare the results
with those for the triangular lattice case.Comment: 4 pages, 2 figure
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