Finite-Size Effects with Boundary Conditions on Bose-Einstein Condensation

We investigate the statistical distribution for ideal Bose gases with constant particle density in the 3D box of volume V=L3. By changing linear size L and imposing different boundary conditions on the system, we present a numerical analysis on the characteristic temperature and condensate fraction and find that a smaller linear size is efficient to increase the characteristic temperature and condensate fraction. Moreover, there is a singularity under the antiperiodic boundary condition.

Thermodynamic limit of the spin-$$ \frac{1}{2} $$ XYZ spin chain with the antiperiodic boundary condition

Based on its off-diagonal Bethe ansatz solution, we study the thermodynamic limit of the spin-$$ \frac{1}{2} $$ 1 2 XYZ spin chain with the antiperiodic boundary condition. The key point of our method is that there exist some degenerate points of the crossing parameter ηm,l, at which the associated inhomogeneous T − Q relation becomes a homogeneous one. This makes extrapolating the formulae deriving from the homogeneous one to an arbitrary η with O(N−2) corrections for a large N possible. The ground state energy and elementary excitations of the system are obtained. By taking the trigonometric limit, we also give the results of antiperiodic XXZ spin chain within the gapless region in the thermodynamic limit, which does not have any degenerate points.

LIGHTFRONT HAMILTONIAN STRUCTURES FOR THE NONLINEAR SIGMA MODEL

We derive the Dirac brackets for the O(N) nonlinear sigma model in the lightfront description with and without constraint. We bring out various subtleties that arise including the fact that antiperiodic boundary condition seems to be preferred.

PHASE STRUCTURES OF THE (2+1)-DIMENSIONAL INFINITE-NCPN−1 MODEL WITH TWISTED BOUNDARY CONDITIONS

We investigate the finite-temperature Néel transitions of the (2+1)-dimensional infinite-NCPN−1 model with a finite spatial dimension. We consider all possible boundary conditions containing the twisted (antiperiodic) one for the imaginary time (inverse temperature) and one finite space: periodic-antiperiodic, antiperiodic-periodic, and antiperiodic-antiperiodic. Simple analytic expressions for the long-range Néel order (LRNO) and the critical line are obtained. Phase diagrams have a region where LRNO appears. Our system can have LRNO even in the infinite-size limit if the imaginary-time axis has the antiperiodic boundary condition.

Degenerate fermion and Wilson loops in 1 + 1 dimensions

We investigate the effect of finite fermion density on symmetry breaking by Wilson loops in (1 + 1) dimensions. We find the breaking and restoration of symmetry at finite density in models with SU(2) and SU(3) gauge symmetries, in the presence of the adjoint fermions. The transition can occur at a finite density of fermions, regardless of the periodic or antiperiodic boundary condition of the fermion field; this is in contrast to the finite-temperature case examined by Ho and Hosotani (IASSNS-HEP preprint 88/48) where the boundary condition of fractional twist is essential to the occurrence of the phase transition.