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