483 research outputs found
An improved discretization of Schrodinger-like radial equations
A new discretization of the radial equations that appear in the solution of
separable second order partial differential equations with some rotational
symmetry (as the Schrodinger equation in a central potential) is presented. It
cures a pathology, related to the singular behaviour of the radial function at
the origin, that suffers in some cases the discretization of the second
derivative with respect to the radial coordinate. This pathology causes an
enormous slowing down of the convergence to the continuum limit when the two
point boundary value problem posed by the radial equation is solved as a
discrete matrix eigenvalue problem. The proposed discretization is a simple
solution to that problem. Some illustrative examples are discussed.Comment: 21 pages, 12 figure
QCD with a theta-vacuum term: a complex system with a simple complex action
We reanalyze in the first part of this paper the old question of P and CT
realization in QCD. The second part is devoted to establish general results on
the phase structure of this model in the presence of a -vacuum term.Comment: 15 pages, to be published in the proceedings of the ``International
Workshop on Non-Perturbative Methods and Lattice QCD'', Guangzhou, China,
15-21 May 200
Theta-vacuum: Phase Transitions and/or Symmetry Breaking at
Assuming that a quantum field theory with a -vacuum term in the
action shows non-trivial -dependence and provided that some reasonable
properties of the probability distribution function of the order parameter
hold, we argue that the theory either breaks spontaneously CP at
or shows a singular behavior at some critical between 0 and .
This result, which applies to any model with a pure imaginary contribution to
the euclidean action consisting in a quantized charge coupled to a phase, as
QCD, is illustrated with two simple examples; one of them intimately related to
Witten's result on SU(N) in the large limit.Comment: 9 pages, 2 figures, 2 references added, final version to appear in
Progr. Theor. Phy
Stability of the skyrmion lattice near the critical temperature in cubic helimagnets
The phase diagram of cubic helimagnets near the critical temperature is
obtained from a Landau-Ginzburg model, including fluctuations to gaussian
level. The free energy is evaluated via a saddle point expansion around the
local minima of the Landau-Ginzburg functional. The local minima are computed
by solving the Euler-Lagrange equations with appropriate boundary conditions,
preserving manifestly the full nonlinearity that is characteristic of skyrmion
states. It is shown that the fluctuations stabilize the skyrmion lattice in a
region of the phase diagram close to the critical temperature, where it becomes
the equilibrium state. A comparison of this approach with previous computations
performed with a different approach (truncated Fourier expansion of magnetic
states) is given.Comment: 6 pages, 6 color figure
Nucleation, instability, and discontinuous phase transitions in monoaxial helimagnets with oblique fields
The phase diagram of the monoaxial chiral helimagnet as a function of
temperature (T ) and magnetic field with components perpendicular (H x ) and
parallel (H z ) to the chiral axis is theoretically studied via the variational
mean field approach in the continuum limit. A phase transition surface in the
three dimensional thermodynamic space separates a chiral spatially modulated
phase from a homogeneous forced ferromagnetic phase. The phase boundary is
divided into three parts: two surfaces of second order transitions of
instability and nucleation type, in De Gennes terminology, are separated by a
surface of first order transitions. Two lines of tricritical points separate
the first order surface from the second order surfaces. The divergence of the
period of the modulated state on the nucleation transition surface has the
logarithmic behavior typical of a chiral soliton lattice. The specific heat
diverges on the nucleation surface as a power law with logarithmic corrections,
while it shows a finite discontinuity on the other two surfaces. The soliton
density curves are described by a universal function of H x if the values of T
and H z determine a transition point lying on the nucleation surface;
otherwise, they are not universal.Comment: Phase diagram refined, with a new tricritical point located; 9 pages,
8 figures; version shortened, published in Phys. Rev.
Understanding the H-T phase diagram of the mono-axial helimagnet
Some unexpected features of the phase diagram of the monoaxial helimagnet in
presence of an applied magnetic field perpendicular to the chiral axis are
theoretically predicted. A rather general hamiltonian with long range
Heisenberg exchange and Dzyaloshinskii--Moriya interactions is considered. The
continuum limit simplifies the free energy, which contains only a few
parameters which in principle are determined by the many parameters of the
hamiltonian, although in practice they may be tuned to fit the experiments. The
phase diagram contains a Chiral Soliton Lattice phase and a forced
ferromagnetic phase separated by a line of phase transitions, which are of
second order at low T and of first order in the vicinity of the zero-field
ordering temperature, and are separated by a tricritical point. A highly non
linear Chiral Soliton Lattice, in which many harmonics contribute appreciably
to the spatial modulation of the local magnetic moment, develops only below the
tricritical temperature, and in this case the scaling shows a logarithmic
behaviour similar to that at T=0, which is a universal feature of the Chiral
Soliton Lattice. Below the tricritical temperature, the normalized soliton
density curves are found to be independent of T, in agreement with the
experimental results of magnetorresistance curves, while above the tricritical
temperature they show a noticeable temperature dependence. The implications in
the interpretation of experimental results of CrNb3S6 are discussed.Comment: 11 pages, 17 figures. Enlarged version, with more details and
results. To be publisehd in Phys. Rev.
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