28 research outputs found
Thermodynamics of the S=1 spin ladder as a composite S=2 chain model
A special class of S=1 spin ladder hamiltonians, with second- neighbor
exchange interactions and with anisotropies in the -direction, can be mapped
onto one-dimensional composite S=2 (tetrahedral S=1) models. We calculate the
high temperature expansion of the Helmoltz free energy for the latter class of
models, and show that their magnetization behaves closely to that of standard
XXZ models with a suitable effective spin , such that
, where refers to the
components of spin in the composite model. It is also shown that the specific
heat per site of the composite model, on the other hand, can be very different
from that of the effective spin model, depending on the parameters of the
hamiltonian.Comment: 17 pages, 4 figures. Submitted for publicatio
Probing singularities in quantum cosmology with curvature scalars
We provide further evidence that the canonical quantization of cosmological
models eliminates the classical Big Bang singularity, using the {\it
DeBroglie-Bohm} interpretation of quantum mechanics. The usual criterion for
absence of the Big Bang singularity in Friedmann-Robertson-Walker quantum
cosmological models is the non-vanishing of the expectation value of the scale
factor. We compute the `local expectation value' of the Ricci and Kretschmann
scalars, for some quantum FRW models. We show that they are finite for all
time. Since these scalars are elements of general scalar polynomials in the
metric and the Riemann tensor, this result indicates that, for the quantum
models treated here, the `local expectation value' of these general scalar
polynomials should be finite everywhere. Therefore, we have further evidence
that the quantization of the models treated here eliminates the classical Big
Bang singularity. PACS: 04.40.Nr, 04.60.Ds, 98.80.Qc.Comment: 9 pages, 6 figure
The high temperature expansion of the classical chain
We present the -expansion of the Helmholtz free energy of the
classical model, with a single-ion anisotropy term and in the presence of
an external magnetic field, up to order . We compare our results to
the numerical solution of Joyce's [Phys. Rev. Lett. 19, 581 (1967)] expression
for the thermodynamics of the classical model, with neither single-ion
anisotropy term nor external magnetic field. This comparison shows that the
derived analytical expansion is valid for intermediate temperatures such as
. We show that the specific heat and magnetic
susceptibility of the spin-2 antiferromagnetic chain can be approximated by
their respective classical results, up to , within an error
of 2.5%. In the absence of an external magnetic field, the ferromagnetic and
antiferromagnetic chains have the same classical Helmholtz free energy. We show
how this two types of media react to the presence of an external magnetic
field
Explorando sistemas hamiltonianos II: pontos de equilíbrio degenerados
Neste segundo artigo sobre sistemas hamiltonianos, apresentamos o método da explosão (blow-up) para a determinação da natureza de pontos fixos (pontos de equilíbrio) degenerados. Aplicamos o método a dois modelos hamiltonianos com um e dois graus de liberdade, respectivamente. Primeiramente, analisamos um sistema formado por um pêndulo simples submetido a um torque externo constante. Em seguida, consideramos um sistema formado por um pêndulo duplo com segmentos de comprimentos e massas iguais, também submetidos a torques externos constantes e não nulos. A presença de pontos de equilíbrio degenerados nos casos dos pêndulos simples e duplo ocorre para certos valores dos torques externos
A Comment on the beta-expansion of s=1/2 and s=1 Ising Models
The purpose of the present work is to apply the method recently developed in
reference [chain_m] to the spin-1 Ising chain, showing how to obtain analytical
-expansions of thermodynamical functions through this formalism. In this
method, we do not solve any transfer matrix-like equations. A comparison
between the -expansions of the specific heat and the magnetic
susceptibility for the and one-dimensional Ising models is
presented. We show that those expansions have poorer convergence when the
auxiliary function of the model has singularities.Comment: 12 pages, 8 figure
On the particle-hole symmetry of the fermionic spinless Hubbard model in D=1
We revisit the particle-hole symmetry of the one-dimensional (D=1) fermionic spinless Hubbard model, associating that symmetry to the invariance of the Helmholtz free energy of the one-dimensional spin-1/2 XXZ Heisenberg model, under reversal of the longitudinal magnetic field and at any finite temperature. Upon comparing two regimes of that chain model so that the number of particles in one regime equals the number of holes in the other, one finds that, in general, their thermodynamics is similar, but not identical: both models share the specific heat and entropy functions, but not the internal energy per site, the first-neighbor correlation functions, and the number of particles per site. Due to that symmetry, the difference between the first-neighbor correlation functions is proportional to the z-component of magnetization of the XXZ Heisenberg model. The results presented in this paper are valid for any value of the interaction strength parameter V, which describes the attractive/null/repulsive interaction of neighboring fermions