1,185 research outputs found
Interacting crumpled manifolds
In this article we study the effect of a delta-interaction on a polymerized
membrane of arbitrary internal dimension D. Depending on the dimensionality of
membrane and embedding space, different physical scenarios are observed. We
emphasize on the difference of polymers from membranes. For the latter,
non-trivial contributions appear at the 2-loop level. We also exploit a
``massive scheme'' inspired by calculations in fixed dimensions for scalar
field theories. Despite the fact that these calculations are only amenable
numerically, we found that in the limit of D to 2 each diagram can be evaluated
analytically. This property extends in fact to any order in perturbation
theory, allowing for a summation of all orders. This is a novel and quite
surprising result. Finally, an attempt to go beyond D=2 is presented.
Applications to the case of self-avoiding membranes are mentioned
Phase transitions of a tethered surface model with a deficit angle term
Nambu-Goto model is investigated by using the canonical Monte Carlo
simulations on fixed connectivity surfaces of spherical topology. Three
distinct phases are found: crumpled, tubular, and smooth. The crumpled and the
tubular phases are smoothly connected, and the tubular and the smooth phases
are connected by a discontinuous transition. The surface in the tubular phase
forms an oblong and one-dimensional object similar to a one-dimensional linear
subspace in the Euclidean three-dimensional space R^3. This indicates that the
rotational symmetry inherent in the model is spontaneously broken in the
tubular phase, and it is restored in the smooth and the crumpled phases.Comment: 6 pages with 6 figure
First-order phase transition in the tethered surface model on a sphere
We show that the tethered surface model of Helfrich and Polyakov-Kleinert
undergoes a first-order phase transition separating the smooth phase from the
crumpled one. The model is investigated by the canonical Monte Carlo
simulations on spherical and fixed connectivity surfaces of size up to N=15212.
The first-order transition is observed when N>7000, which is larger than those
in previous numerical studies, and a continuous transition can also be observed
on small-sized surfaces. Our results are, therefore, consistent with those
obtained in previous studies on the phase structure of the model.Comment: 6 pages with 7 figure
Topological lattice actions for the 2d XY model
We consider the 2d XY Model with topological lattice actions, which are invariant against small deformations of the field configuration. These actions constrain the angle between neighbouring spins by an upper bound, or they explicitly suppress vortices (and anti-vortices). Although topological actions do not have a classical limit, they still lead to the universal behaviour of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition - at least up to moderate vortex suppression. In the massive phase, the analytically known Step Scaling Function (SSF) is reproduced in numerical simulations. However, deviations from the expected universal behaviour of the lattice artifacts are observed. In the massless phase, the BKT value of the critical exponent eta(c) is confirmed. Hence, even though for some topological actions vortices cost zero energy, they still drive the standard BKT transition. In addition we identify a vortex-free transition point, which deviates from the BKT behaviour
Phase transitions of an intrinsic curvature model on dynamically triangulated spherical surfaces with point boundaries
An intrinsic curvature model is investigated using the canonical Monte Carlo
simulations on dynamically triangulated spherical surfaces of size upto N=4842
with two fixed-vertices separated by the distance 2L. We found a first-order
transition at finite curvature coefficient \alpha, and moreover that the order
of the transition remains unchanged even when L is enlarged such that the
surfaces become sufficiently oblong. This is in sharp contrast to the known
results of the same model on tethered surfaces, where the transition weakens to
a second-order one as L is increased. The phase transition of the model in this
paper separates the smooth phase from the crumpled phase. The surfaces become
string-like between two point-boundaries in the crumpled phase. On the
contrary, we can see a spherical lump on the oblong surfaces in the smooth
phase. The string tension was calculated and was found to have a jump at the
transition point. The value of \sigma is independent of L in the smooth phase,
while it increases with increasing L in the crumpled phase. This behavior of
\sigma is consistent with the observed scaling relation \sigma \sim (2L/N)^\nu,
where \nu\simeq 0 in the smooth phase, and \nu=0.93\pm 0.14 in the crumpled
phase. We should note that a possibility of a continuous transition is not
completely eliminated.Comment: 15 pages with 10 figure
Two-Hole Bound States from a Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet
Identifying the correct low-energy effective theory for magnons and holes in
an antiferromagnet has remained an open problem for a long time. In analogy to
the effective theory for pions and nucleons in QCD, based on a symmetry
analysis of Hubbard and t-J-type models, we construct a systematic low-energy
effective field theory for magnons and holes located inside pockets centered at
lattice momenta (\pm pi/2a,\pm pi/2a). The effective theory is based on a
nonlinear realization of the spontaneously broken spin symmetry and makes
model-independent universal predictions for the entire class of lightly doped
antiferromagnetic precursors of high-temperature superconductors. The
predictions of the effective theory are exact, order by order in a systematic
low-energy expansion. We derive the one-magnon exchange potentials between two
holes in an otherwise undoped system. Remarkably, in some cases the
corresponding two-hole Schr\"odinger equations can even be solved analytically.
The resulting bound states have d-wave characteristics. The ground state wave
function of two holes residing in different hole pockets has a d_{x^2-y^2}-like
symmetry, while for two holes in the same pocket the symmetry resembles d_{xy}.Comment: 35 pages, 11 figure
Precision study of 6p 2Pj - 8s 2S1/2 relative transition matrix elements in atomic Cs
A combined experimental and theoretical study of transition matrix elements
of the 6p 2Pj - 8s 2S1/2 transition in atomic Cs is reported. Measurements of
the polarization-dependent two-photon excitation spectrum associated with the
transition were made in an approximately 200 cm-1 range on the low frequency
side of the 6s 2S1/2 - 6p 2P3/2 resonance. The measurements depend
parametrically on the relative transition matrix elements, but also are
sensitive to far-off-resonance 6s 2S1/2 - np 2Pj - 8s 2S1/2 transitions. In the
past, this dependence has yielded a generalized sum rule, the value of which is
dependent on sums of relative two-photon transition matrix elements. In the
present case, best available determinations from other experiments are combined
with theoretical matrix elements to extract the ratio of transition matrix
elements for the 6p 2Pj - 8s 2S1/2 (j = 1/2,3/2) transition. The resulting
experimental value of 1.423(2) is in excellent agreement with the theoretical
value, calculated using a relativistic all-order method, of 1.425(2)
Critical exponents of the quantum phase transition in a planar antiferromagnet
We have performed a large scale quantum Monte Carlo study of the quantum
phase transition in a planar spin-1/2 Heisenberg antiferromagnet with CaV4O9
structure. We obtain a dynamical exponent z=1.018+/-0.02. The critical
exponents beta, nu and eta agree within our errors with the classical 3D O(3)
exponents, expected from a mapping to the nonlinear sigma model. This confirms
the conjecture of Chubukov, Sachdev and Ye [Phys. Rev. B 49, 11919 (1994)] that
the Berry phase terms in the planar Heisenberg antiferromagnet are dangerously
irrelevant.Comment: 5 pages including 4 figures; revised version: some minor changes and
added reference
Dimensional Reduction of Fermions in Brane Worlds of the Gross-Neveu Model
We study the dimensional reduction of fermions, both in the symmetric and in
the broken phase of the 3-d Gross-Neveu model at large N. In particular, in the
broken phase we construct an exact solution for a stable brane world consisting
of a domain wall and an anti-wall. A left-handed 2-d fermion localized on the
domain wall and a right-handed fermion localized on the anti-wall communicate
with each other through the 3-d bulk. In this way they are bound together to
form a Dirac fermion of mass m. As a consequence of asymptotic freedom of the
2-d Gross-Neveu model, the 2-d correlation length \xi = 1/m increases
exponentially with the brane separation. Hence, from the low-energy point of
view of a 2-d observer, the separation of the branes appears very small and the
world becomes indistinguishable from a 2-d space-time. Our toy model provides a
mechanism for brane stabilization: branes made of fermions may be stable due to
their baryon asymmetry. Ironically, our brane world is stable only if it has an
extreme baryon asymmetry with all states in this ``world'' being completely
filled.Comment: 26 pages, 7 figure
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