43 research outputs found
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
Solutions for correlations along the coexistence curve and at the critical point of a kagom\'e lattice gas with three-particle interactions
We consider a two-dimensional (d=2) kagom\'e lattice gas model with
attractive three-particle interactions around each triangular face of the
kagom\'e lattice. Exact solutions are obtained for multiparticle correlations
along the liquid and vapor branches of the coexistence curve and at
criticality. The correlation solutions are also determined along the
continuation of the curvilinear diameter of the coexistence region into the
disordered fluid region. The method generates a linear algebraic system of
correlation identities with coefficients dependent only upon the interaction
parameter. Using a priori knowledge of pertinent solutions for the density and
elementary triplet correlation, one finds a closed and linearly independent set
of correlation identities defined upon a spatially compact nine-site cluster of
the kagom\'e lattice. Resulting exact solution curves of the correlations are
plotted and discussed as functions of the temperature, and are compared with
corresponding results in a traditional kagom\'e lattice gas having
nearest-neighbor pair interactions. An example of application for the
multiparticle correlations is demonstrated in cavitation theory
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
"The Ising model on spherical lattices: dimer versus Monte Carlo approach"
We study, using dimer and Monte Carlo approaches, the critical properties and
finite size effects of the Ising model on honeycomb lattices folded on the
tetrahedron. We show that the main critical exponents are not affected by the
presence of conical singularities. The finite size scaling of the position of
the maxima of the specific heat does not match, however, with the scaling of
the correlation length, and the thermodynamic limit is attained faster on the
spherical surface than in corresponding lattices on the torus.Comment: 25 pages + 6 figures not included. Latex file. FTUAM 93-2
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
Gas of self-avoiding loops on the brickwork lattice
An exact calculation of the phase diagram for a loop gas model on the
brickwork lattice is presented. The model includes a bending energy. In the
dense limit, where all the lattice sites are occupied, a phase transition
occuring at an asymmetric Lifshitz tricritical point is observed as the
temperature associated with the bending energy is varied. Various critical
exponents are calculated. At lower densities, two lines of transitions (in the
Ising universality class) are observed, terminated by a tricritical point,
where there is a change in the modulation of the correlation function. To each
tricritical point an associated disorder line is found.Comment: 19 pages, 6 figures. to appear in J. Phys. A : Math. & Ge
Ordering in Two-Dimensional Ising Models with Competing Interactions
We study the 2D Ising model on a square lattice with additional non-equal
diagonal next-nearest neighbor interactions. The cases of classical and quantum
(transverse) models are considered. Possible phases and their locations in the
space of three Ising couplings are analyzed. In particular, incommensurate
phases occurring only at non-equal diagonal couplings, are predicted. We also
analyze a spin-pseudospin model comprised of the quantum Ising model coupled to
XY spin chains in a particular region of interactions, corresponding to the
Ising sector's super-antiferromagnetic (SAF) ground state. The spin-SAF
transition in the coupled Ising-XY model into a phase with co-existent SAF
Ising (pseudospin) long-range order and a spin gap is considered. Along with
destruction of the quantum critical point of the Ising sector, the phase digram
of the Ising-XY model can also demonstrate a re-entrance of the spin-SAF phase.
A detailed study of the latter is presented. The mechanism of the re-entrance,
due to interplay of interactions in the coupled model, and the conditions of
its appearance are established. Applications of the spin-SAF theory for the
transition in the quarter-filled ladder compound NaV2O5 are discussed.Comment: Minor revisions and refs. added; published version of the invited
paper in a special issue of "Low Temp. Physics
Spinons in a Crossed-Chains Model of a 2D Spin Liquid
Using Random Phase Approximation, we show that a crossed-chains model of a
spin-1/2 Heisenberg spins, with frustrated interchain couplings, has a
non-dimerized spin-liquid ground state in 2D, with deconfined spinons as the
elementary excitations. The results are confirmed by a bosonization study,
which shows that the system is an example of a `sliding Luttinger liquid'. In
an external field, the system develops an incommensurate field-induced long
range order with a finite transition temperature.Comment: 4 pages, 3 figures; added references; scaling analysis, preserving
spin rotational invariance, is extended to finite temperatur
Finite-size scaling and conformal anomaly of the Ising model in curved space
We study the finite-size scaling of the free energy of the Ising model on
lattices with the topology of the tetrahedron and the octahedron. Our
construction allows to perform changes in the length scale of the model without
altering the distribution of the curvature in the space. We show that the
subleading contribution to the free energy follows a logarithmic dependence, in
agreement with the conformal field theory prediction. The conformal anomaly is
given by the sum of the contributions computed at each of the conical
singularities of the space, except when perfect order of the spins is precluded
by frustration in the model.Comment: 4 pages, 4 Postscript figure
Complex-Temperature Singularities in the Ising Model. III. Honeycomb Lattice
We study complex-temperature properties of the uniform and staggered
susceptibilities and of the Ising model on the honeycomb
lattice. From an analysis of low-temperature series expansions, we find
evidence that and both have divergent singularities at the
point (where ), with exponents
. The critical amplitudes at this
singularity are calculated. Using exact results, we extract the behaviour of
the magnetisation and specific heat at complex-temperature
singularities. We find that, in addition to its zero at the physical critical
point, diverges at with exponent , vanishes
continuously at with exponent , and vanishes
discontinuously elsewhere along the boundary of the complex-temperature
ferromagnetic phase. diverges at with exponent
and at (where ) with exponent , and
diverges logarithmically at . We find that the exponent relation
is violated at ; the right-hand side is 4
rather than 2. The connections of these results with complex-temperature
properties of the Ising model on the triangular lattice are discussed.Comment: 22 pages, latex, figures appended after the end of the text as a
compressed, uuencoded postscript fil