29 research outputs found
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
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
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
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
Reflections on the four facets of symmetry: how physics exemplifies rational thinking
In contemporary theoretical physics, the powerful notion of symmetry stands
for a web of intricate meanings among which I identify four clusters associated
with the notion of transformation, comprehension, invariance and projection.
While their interrelations are examined closely, these four facets of symmetry
are scrutinised one after the other in great detail. This decomposition allows
us to examine closely the multiple different roles symmetry plays in many
places in physics. Furthermore, some connections with others disciplines like
neurobiology, epistemology, cognitive sciences and, not least, philosophy are
proposed in an attempt to show that symmetry can be an organising principle
also in these fields
The Ising Susceptibility Scaling Function
We have dramatically extended the zero field susceptibility series at both
high and low temperature of the Ising model on the triangular and honeycomb
lattices, and used these data and newly available further terms for the square
lattice to calculate a number of terms in the scaling function expansion around
both the ferromagnetic and, for the square and honeycomb lattices, the
antiferromagnetic critical point.Comment: PDFLaTeX, 50 pages, 5 figures, zip file with series coefficients and
background data in Maple format provided with the source files. Vs2: Added
dedication and made several minor additions and corrections. Vs3: Minor
corrections. Vs4: No change to eprint. Added essential square-lattice series
input data (used in the calculation) that were removed from University of
Melbourne's websit