69 research outputs found
Kink confinement in the antiferromagnetic XXZ spin-1/2 chain in a weak staggered magnetic field
The Heisenberg XXZ spin-1/2 chain is considered in the massive
antiferromagnetic regime in the presence of a staggered longitudinal magnetic
field. The Hamiltonian of the model is characterised by the anisotropy
parameter , and by the magnetic field strength h. At zero magnetic
field, the model is exactly solvable. In the thermodynamic limit, it has two
degenerate vacua and the kinks (which are also called spinons) interpolating
between these vacua, as elementary excitations. Application of the staggered
magnetic field breaks integrability of the model and induces the long-range
attractive potential between two adjacent kinks leading to their confinement
into the bound states. The energy spectra of the resulting two-kink bound
states are perturbatively calculated in the extreme anisotropic (Ising) limit
to the first order in the inverse anisotropy constant
, and also for generic values of to the first order
in the weak magnetic field h.Comment: publishes version, minor changes, misprints correcte
Monte-Carlo simulation of nucleation in the two-dimensional Potts model
Nucleation in the two-dimensional q-state Potts model has been studied by
means of Monte-Carlo simulations using the heat-bath dynamics. The initial
metastable state has been prepared by magnetic quench of the ordered
low-temperature phase. The magnetic field dependence of the nucleation time has
been measured as the function of the magnetic field for different q and lattice
sizes at T=0.5 Tc. A size-dependent crossover from the coalescence to
nucleation region is observed at all q. The magnetic field dependence of the
nucleation time is roughly described by the classical nucleation theory. Our
data show increase of the anisotropy in the shape of the critical droplets with
increase of q.Comment: 15 pages LaTeX, 10 figure
Confinement of spinons in the XXZ spin-1/2 chain in presence of the transverse magnetic field
We study the tuning effect of a transverse magnetic field on the confinement
of spinons in the infinite XXZ spin-1/2 chain. The spinon confinement in this
model takes place in the gapped antiferromagnetic phase upon application of a
staggered longitudinal magnetic field. The tuning transverse magnetic field has
mutually orthogonal uniform and staggered components. The energy spectra of the
two-spinon bound states (the `mesons') in the confinement regime are
analytically calculated in this model using two different perturbative schemes.
The first one applies in the extreme anisotropic (Ising) limit and employs the
inverse anisotropy constant as a small parameter. The second perturbative
scheme, which applies at any anisotropy in the gapped antiferromagnetic domain,
exploits the integrability of the XXZ spin chain at zero magnetic field. The
small parameters in the second technique are the components of the transverse,
and staggered longitudinal magnetic fields. It is shown, that the weak
transverse magnetic field mixes the transverse and longitudinal meson modes,
and leads to an avoided crossing of their energies upon increase of its
strength. The explicit formulas for the two-spinon contribution to the
dynamical structure factors of local spin operators are obtained as well in
this model in the weak confinement regime for wave-vectors close to the points
k = 0 and k = \pi.Comment: v3: 38 pages, 14 figures. One section added, misprints correcte
On the weak confinement of kinks in the one-dimensional quantum ferromagnet CoNb2O6
In a recent paper Coldea et al (2010 Science {\bf 327} 177) report
observation of the weak confinement of kinks in the Ising spin chain
ferromagnet CoNb2O6 at low temperatures. To interpret the entire spectra of
magnetic excitations measured via neutron scattering, they introduce a
phenomenological model, which takes into account only the two-kink
configurations of the spin chain. We present the exact solution of this model.
The explicit expressions for the two-kink bound-state energy spectra and for
the relative intensities of neutron scattering on these magnetic modes are
obtained in terms of the Bessel function.Comment: 18 pages, 9 figures; v2: figures 1,3,4 replaced, few misprints
correcte
Two-kink bound states in the magnetically perturbed Potts field theory at T<Tc
The q-state Potts field theory with in the low-temperature
phase is considered in presence of a weak magnetic field h. In absence of the
magnetic field, the theory is integrable, but not free at q>2: its elementary
excitations - the kinks - interact at small distances, and their interaction
can be characterized by the factorizable scattering matrix which was found by
Chim and Zamolodchikov. The magnetic field induces the long-range attraction
between kinks causing their confinement into the bound-states. We calculate the
masses of the two-kink bound states in the leading order in |h| -> 0 expressing
them in terms of the scattering matrix of kinks at h=0.Comment: 20 pages, no figures, v2: one section and references adde
Decay of the metastable phase in d=1 and d=2 Ising models
We calculate perturbatively the tunneling decay rate of the
metastable phase in the quantum d=1 Ising model in a skew magnetic field near
the coexistence line at T=0. It is shown that
oscillates in the magnetic field due to discreteness of the excitation
energy spectrum. After mapping of the obtained results onto the extreme
anisotropic d=2 Ising model at , we verify in the latter model the
droplet theory predictions for the free energy analytically continued to the
metastable phase. We find also evidence for the discrete-lattice corrections in
this metastable phase free energy.Comment: 4 pages, REVTe
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