1,065 research outputs found
Probing Vortex Unbinding via Dipole Fluctuations
We develop a numerical method for detecting a vortex unbinding transition in
a two-dimensional system by measuring large scale fluctuations in the total
vortex dipole moment of the system. These are characterized by a
quantity which measures the number of configurations in a simulation
for which the either or is half the system size. It is shown that
tends to a non-vanishing constant for large system sizes in the
unbound phase, and vanishes in the bound phase. The method is applied to the XY
model both in the absence and presence of a magnetic field. In the latter case,
the system size dependence of suggests that there exist three distinct
phases, one unbound vortex phase, a logarithmically bound phase, and a linearly
bound phase.Comment: 6 pages, 2 figure
Defect fugacity, Spinwave Stiffness and T_c of the 2-d Planar Rotor Model
We obtain precise values for the fugacities of vortices in the 2-d planar
rotor model from Monte Carlo simulations in the sector with {\em no} vortices.
The bare spinwave stiffness is also calculated and shown to have significant
anharmonicity. Using these as inputs in the KT recursion relations, we predict
the temperature T_c = 0.925, using linearised equations, and using next higher order corrections, at which vortex unbinding commences
in the unconstrained system. The latter value, being in excellent agreement
with all recent determinations of T_c, demonstrates that our method 1)
constitutes a stringent measure of the relevance of higher order terms in KT
theory and 2) can be used to obtain transition temperatures in similar systems
with modest computational effort.Comment: 7 pages, 4 figure
A Renormalization Group Analysis of Coupled Superconducting and Stripe Order in 1+1 Dimensions
In this paper we perform a renormalization group analysis on the 1+1
dimensional version of an effective field theory (previously proposed by
Dung-Hai Lee, cond-mat/011393) describing (quantum) fluctuating stripe and
superconductor orders. We find four possible phases corresponding to stripe
order/disorder combined with superconducting order/disorder.Comment: 8 pages, 3 figures, revte
Correlations in the low-temperature phase of the two-dimensional XY model
Monte Carlo simulations of the two-dimensional XY model are performed in a
square geometry with fixed boundary conditions. Using a conformal mapping it is
very easy to deduce the exponent eta_sigma(T) of the order parameter
correlation function at any temperature in the critical phase of the model. The
temperature behaviour of eta_sigma(T) is obtained numerically with a good
accuracy up to the Kosterlitz-Thouless transition temperature. At very low
temperatures, a good agreement is found with Berezinskii's harmonic
approximation. Surprisingly, we show some evidence that there are no
logarithmic corrections to the behaviour of the order parameter density profile
(with symmetry breaking surface fields) at the Kosterlitz-Thouless transition
temperature.Comment: 7 pages, 2 eps figure
The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
We study the classical XY (plane rotator) model at the Kosterlitz-Thouless
phase transition. We simulate the model using the single cluster algorithm on
square lattices of a linear size up to L=2048.We derive the finite size
behaviour of the second moment correlation length over the lattice size
xi_{2nd}/L at the transition temperature. This new prediction and the analogous
one for the helicity modulus are confronted with our Monte Carlo data. This way
beta_{KT}=1.1199 is confirmed as inverse transition temperature. Finally we
address the puzzle of logarithmic corrections of the magnetic susceptibility
chi at the transition temperature.Comment: Monte Carlo results for xi/L in table 1 and 2 corrected. Due to a
programming error,these numbers were wrong by about a factor 1+1/L^2.
Correspondingly the fits with L_min=64 and 128 given in table 5 and 6 are
changed by little.The central results of the paper are not affected. Wrong
sign in eq.(52) corrected. Appendix extende
Direct Evidence of the Discontinuous Character of the Kosterlitz-Thouless Jump
It is numerically shown that the discontinuous character of the helicity
modulus of the two-dimensional XY model at the Kosterlitz-Thouless (KT)
transition can be directly related to a higher order derivative of the free
energy without presuming any {\it a priori} knowledge of the nature of the
transition. It is also suggested that this higher order derivative is of
intrinsic interest in that it gives an additional characteristics of the KT
transition which might be associated with a universal number akin to the
universal value of the helicity modulus at the critical temperature.Comment: 4 pages, to appear in PR
Density-functional fidelity approach to quantum phase transitions
We propose a new approach to quantum phase transitions in terms of the
density-functional fidelity, which measures the similarity between density
distributions of two ground states in parameter space. The key feature of the
approach, as we will show, is that the density-functional fidelity can be
measured easily in experiments. Both the validity and versatility of the
approach are checked by the Lipkin-Meshkov-Glick model and the one-dimensional
Hubbard model.Comment: 4 pages, 2 figures, submitted to Chin. Phys. Let
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