65 research outputs found
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 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
"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
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
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
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
Equilibrium and dynamical properties of the ANNNI chain at the multiphase point
We study the equilibrium and dynamical properties of the ANNNI (axial
next-nearest-neighbor Ising) chain at the multiphase point. An interesting
property of the system is the macroscopic degeneracy of the ground state
leading to finite zero-temperature entropy. In our equilibrium study we
consider the effect of softening the spins. We show that the degeneracy of the
ground state is lifted and there is a qualitative change in the low temperature
behaviour of the system with a well defined low temperature peak of the
specific heat that carries the thermodynamic ``weight'' of the ground state
entropy. In our study of the dynamical properties, the stochastic Kawasaki
dynamics is considered. The Fokker-Planck operator for the process corresponds
to a quantum spin Hamiltonian similar to the Heisenberg ferromagnet but with
constraints on allowed states. This leads to a number of differences in its
properties which are obtained through exact numerical diagonalization,
simulations and by obtaining various analytic bounds.Comment: 9 pages, RevTex, 6 figures (To appear in Phys. Rev. E
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
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