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 $\Delta<-1$, 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 $\Delta\to-\infty$ to the first order in the inverse anisotropy constant $|\Delta|^{-1}$, and also for generic values of $\Delta<-1$ 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

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 $2\le q\le 4$ 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 $\Gamma$ of the metastable phase in the quantum d=1 Ising model in a skew magnetic field near the coexistence line $0<h_{x}<1, h_{z}\to -0$ at T=0. It is shown that $\Gamma$ oscillates in the magnetic field $h_{z}$ due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic d=2 Ising model at $T<T_c$, 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

ADAPTATION OF THE RESULTS AT TRANSFER BY CALQUE

Статья посвящена проблеме адаптации перевода в системе своеязычных лексических, фразеологических, словообразовательных, грамматических, стилистических средств. Массу подтверждений необходимости, важности, адаптирования своеязычного наименования автор находит в массиве белорусских калек с русских слов и устойчивых словосочетаний.The article is devoted to the problem of adapting the translation in the system of peculiar language, phraseological, word-formation, grammatical, stylistic means. The author finds the mass of evidence of the necessity, importance, and adaptation of his own language in the array of Belarusian cripples with Russian words and stable phrases