1,513 research outputs found
Conducting-angle-based percolation in the XY model
We define a percolation problem on the basis of spin configurations of the
two dimensional XY model. Neighboring spins belong to the same percolation
cluster if their orientations differ less than a certain threshold called the
conducting angle. The percolation properties of this model are studied by means
of Monte Carlo simulations and a finite-size scaling analysis. Our simulations
show the existence of percolation transitions when the conducting angle is
varied, and we determine the transition point for several values of the XY
coupling. It appears that the critical behavior of this percolation model can
be well described by the standard percolation theory. The critical exponents of
the percolation transitions, as determined by finite-size scaling, agree with
the universality class of the two-dimensional percolation model on a uniform
substrate. This holds over the whole temperature range, even in the
low-temperature phase where the XY substrate is critical in the sense that it
displays algebraic decay of correlations.Comment: 16 pages, 14 figure
Exact characterization of O(n) tricriticality in two dimensions
We propose exact expressions for the conformal anomaly and for three critical
exponents of the tricritical O(n) loop model as a function of n in the range
. These findings are based on an analogy with known
relations between Potts and O(n) models, and on an exact solution of a
'tri-tricritical' Potts model described in the literature. We verify the exact
expressions for the tricritical O(n) model by means of a finite-size scaling
analysis based on numerical transfer-matrix calculations.Comment: submitted to Phys. Rev. Let
Phase Diagram of a Loop on the Square Lattice
The phase diagram of the O(n) model, in particular the special case , is
studied by means of transfer-matrix calculations on the loop representation of
the O(n) model. The model is defined on the square lattice; the loops are
allowed to collide at the lattice vertices, but not to intersect. The loop
model contains three variable parameters that determine the loop density or
temperature, the energy of a bend in a loop, and the interaction energy of
colliding loop segments. A finite-size analysis of the transfer-matrix results
yields the phase diagram in a special plane of the parameter space. These
results confirm the existence of a multicritical point and an Ising-like
critical line in the low-temperature O(n) phase.Comment: LaTeX, 3 eps file
First and second order transitions in dilute O(n) models
We explore the phase diagram of an O(n) model on the honeycomb lattice with
vacancies, using finite-size scaling and transfer-matrix methods. We make use
of the loop representation of the O(n) model, so that is not restricted to
positive integers. For low activities of the vacancies, we observe critical
points of the known universality class. At high activities the transition
becomes first order. For n=0 the model includes an exactly known theta point,
used to describe a collapsing polymer in two dimensions. When we vary from
0 to 1, we observe a tricritical point which interpolates between the
universality classes of the theta point and the Ising tricritical point.Comment: LaTeX, 6 eps file
Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the Potts model
By relating the ground state of Temperley-Lieb hamiltonians to partition
functions of 2D statistical mechanics systems on a half plane, and using a
boundary Coulomb gas formalism, we obtain in closed form the valence bond
entanglement entropy as well as the valence bond probability distribution in
these ground states. We find in particular that for the XXX spin chain, the
number N_c of valence bonds connecting a subsystem of size L to the outside
goes, in the thermodynamic limit, as = (4/pi^2) ln L, disproving a recent
conjecture that this should be related with the von Neumann entropy, and thus
equal to 1/(3 ln 2) ln L. Our results generalize to the Q-state Potts model.Comment: 4 pages, 2 figure
End to end distance on contour loops of random gaussian surfaces
A self consistent field theory that describes a part of a contour loop of a
random Gaussian surface as a trajectory interacting with itself is constructed.
The exponent \nu characterizing the end to end distance is obtained by a Flory
argument. The result is compared with different previuos derivations and is
found to agree with that of Kondev and Henley over most of the range of the
roughening exponent of the random surface.Comment: 7 page
Angular spectrum of quantized light beams
We introduce a generalized angular spectrum representation for quantized
light beams. By using our formalism, we are able to derive simple expressions
for the electromagnetic vector potential operator in the case of: {a)}
time-independent paraxial fields, {b)} time-dependent paraxial fields, and {c)}
non-paraxial fields. For the first case, the well known paraxial results are
fully recovered.Comment: 3 pages, no figure
A constrained Potts antiferromagnet model with an interface representation
We define a four-state Potts model ensemble on the square lattice, with the
constraints that neighboring spins must have different values, and that no
plaquette may contain all four states. The spin configurations may be mapped
into those of a 2-dimensional interface in a 2+5 dimensional space. If this
interface is in a Gaussian rough phase (as is the case for most other models
with such a mapping), then the spin correlations are critical and their
exponents can be related to the stiffness governing the interface fluctuations.
Results of our Monte Carlo simulations show height fluctuations with an
anomalous dependence on wavevector, intermediate between the behaviors expected
in a rough phase and in a smooth phase; we argue that the smooth phase (which
would imply long-range spin order) is the best interpretation.Comment: 61 pages, LaTeX. Submitted to J. Phys.
Geometric phases in astigmatic optical modes of arbitrary order
The transverse spatial structure of a paraxial beam of light is fully
characterized by a set of parameters that vary only slowly under free
propagation. They specify bosonic ladder operators that connect modes of
different order, in analogy to the ladder operators connecting
harmonic-oscillator wave functions. The parameter spaces underlying sets of
higher-order modes are isomorphic to the parameter space of the ladder
operators. We study the geometry of this space and the geometric phase that
arises from it. This phase constitutes the ultimate generalization of the Gouy
phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the
geometric phase of non-astigmatic optical modes with orbital angular momentum
states in limiting cases. We briefly discuss the well-known analogy between
geometric phases and the Aharonov-Bohm effect, which provides some
complementary insights in the geometric nature and origin of the generalized
Gouy phase shift. Our method also applies to the quantum-mechanical description
of wave packets. It allows for obtaining complete sets of normalized solutions
of the Schr\"odinger equation. Cyclic transformations of such wave packets give
rise to a phase shift, which has a geometric interpretation in terms of the
other degrees of freedom involved.Comment: final versio
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