21 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
Berry's Phase in the Presence of a Dissipative Medium
We consider the spin 1/2 model coupled to a slowly varying magnetic field in
the presence of a weak damping represented by a Lindblad-form operators. We
show that Berry's geometrical phase remains unaltered by the two dissipation
mechanism considered. Dissipation effects are twofold: a shrinking in the
modulus of the Bloch's vector, which characterizes coherence loss and a time
dependent (dissipation related) precession angle. We show that the line
broadening of the Fourier transformation of the components of magnetization is
only due to the presence of dissipation.Comment: 19 pages, 2 figure
Adiabatic Approximation in the Density Matrix Approach: Non-Degenerate Systems
We study the adiabatic limit in the density matrix approach for a quantum
system coupled to a weakly dissipative medium. The energy spectrum of the
quantum model is supposed to be non-degenerate. In the absence of dissipation,
the geometric phases for periodic Hamiltonians obtained previously by M.V.
Berry are recovered in the present approach. We determine the necessary
condition satisfied by the coefficients of the linear expansion of the
non-unitary part of the Liouvillian in order to the imaginary phases acquired
by the elements of the density matrix, due to dissipative effects, be
geometric. The results derived are model-independent. We apply them to spin 1/2
model coupled to reservoir at thermodynamic equilibrium.Comment: 24 pages (new version), accepted for publication in Physica
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
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
Water level effect on herbaceous plant assemblages at an artificial reservoir-Lago Azul State Park, Southern Brazil
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
The β-expansion of the D=1 fermionic spinless Hubbard model off the half-filling regime
We obtain that when the spinless model is off the half-filling regime (μ ≠ V), the Helmholtz free energy (HFE) can be written as two β-expansions: one expansion comes from the half-filling configuration and another one that depends on the parameter x = μ - V. We show numerically that the chemical potential as a function of temperature satisfies a relation similar to one derived from the particle-hole symmetry of the fermionic spinless model. We extend the β-expansion of the HFE of the one-dimensional fermionic spinless Hubbard model up to order β8