1,462 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
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
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
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
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
Worm Algorithm for Continuous-space Path Integral Monte Carlo Simulations
We present a new approach to path integral Monte Carlo (PIMC) simulations
based on the worm algorithm, originally developed for lattice models and
extended here to continuous-space many-body systems. The scheme allows for
efficient computation of thermodynamic properties, including winding numbers
and off-diagonal correlations, for systems of much greater size than that
accessible to conventional PIMC. As an illustrative application of the method,
we simulate the superfluid transition of Helium-four in two dimensions.Comment: Fig. 2 differs from that of published version (includes data for
larger system sizes
Properties of Phase transitions of a Higher Order
The following is a thermodynamic analysis of a III order (and some aspects of
a IV order) phase transition. Such a transition can occur in a superconductor
if the normal state is a diamagnet. The equation for a phase boundary in an H-T
(H is the magnetic field, T, the temperature) plane is derived. by considering
two possible forms of the gradient energy, it is possible to construct a field
theory which describes a III or a IV order transition and permits a study of
thermal fluctuations and inhomogeneous order parameters.Comment: 13 pages, revtex, no figure
Criticality in one dimension with inverse square-law potentials
It is demonstrated that the scaled order parameter for ferromagnetic Ising
and three-state Potts chains with inverse-square interactions exhibits a
universal critical jump, in analogy with the superfluid density in helium
films. Renormalization-group arguments are combined with numerical simulations
of systems containing up to one million lattice sites to accurately determine
the critical properties of these models. In strong contrast with earlier work,
compelling quantitative evidence for the Kosterlitz--Thouless-like character of
the phase transition is provided.Comment: To appear in Phys. Rev. Let
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