1,457 research outputs found

### Wave-function renormalization for the Coulomb-gas in Wegner-Houghton's RG method

The RG flow for the sine-Gordon model is determined by means of the method of
Wegner and Houghton in next-to-leading order of the derivative expansion. For
small values of the fugacity this agrees with the well-known RG flow of the
two-dimensional Coulomb-gas found in the dilute gas approximation and a
systematic way of obtaining higher-order corrections to this approximation is
given.Comment: 4 pages, 2 figure

### 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

### 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 $T_c = 0.899 \pm
>.005$ 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

### 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

### The Lattice $\beta$-function of Quantum Spin Chains

We derive the lattice $\beta$-function for quantum spin chains, suitable for
relating finite temperature Monte Carlo data to the zero temperature fixed
points of the continuum nonlinear sigma model. Our main result is that the
asymptotic freedom of this lattice $\beta$-function is responsible for the
nonintegrable singularity in $\theta$, that prevents analytic continuation
between $\theta=0$ and $\theta=\pi$.Comment: 10 page

### An alternative field theory for the Kosterlitz-Thouless transition

We extend a Gaussian model for the internal electrical potential of a
two-dimensional Coulomb gas by a non-Gaussian measure term, which singles out
the physically relevant configurations of the potential. The resulting
Hamiltonian, expressed as a functional of the internal potential, has a
surprising large-scale limit: The additional term simply counts the number of
maxima and minima of the potential. The model allows for a transparent
derivation of the divergence of the correlation length upon lowering the
temperature down to the Kosterlitz-Thouless transition point.Comment: final version, extended discussion, appendix added, 8 pages, no
figure, uses IOP documentclass iopar

### Bimerons in Double Layer Quantum Hall Systems

In this paper we discuss bimeron pseudo spin textures for double layer
quantum hall systems with filling factor $\nu =1$. Bimerons are excitations
corresponding to bound pairs of merons and anti-merons.
Bimeron solutions have already been studied at great length by other groups
by minimising the microsopic Hamiltonian between microscopic trial
wavefunctions. Here we calculate them by numerically solving coupled nonlinear
partial differential equations arising from extremisation of the effective
action for pseudospin textures. We also calculate the different contributions
to the energy of our bimerons, coming from pseudospin stiffness, capacitance
and coulomb interactions between the merons. Apart from augmenting earlier
results, this allows us to check how good an approximation it is to think of
the bimeron as a pair of rigid objects (merons) with logarithmically growing
energy, and with electric charge ${1 \over 2}$. Our differential equation
approach also allows us to study the dependence of the spin texture as a
function of the distance between merons, and the inter layer distance. Lastly,
the technical problem of solving coupled nonlinear partial differential
equations, subject to the special boundary conditions of bimerons is
interesting in its own right.Comment: 8 ps figures included; to be published in IJMP

### First-order phase transitions in two-dimensional off-lattice liquid crystals

We consider an off-lattice liquid crystal pair potential in strictly two
dimensions. The potential is purely repulsive and short-ranged. Nevertheless,
by means of a single parameter in the potential, the system is shown to undergo
a first-order phase transition. The transition is studied using mean-field
density functional theory, and shown to be of the isotropic-to-nematic kind. In
addition, the theory predicts a large density gap between the two coexisting
phases. The first-order nature of the transition is confirmed using computer
simulation and finite-size scaling. Also presented is an analysis of the
interface between the coexisting domains, including estimates of the line
tension, as well as an investigation of anchoring effects.Comment: 12 pages, 17 figures, submitted to J. Phys.: Condens. Matte

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