138 research outputs found
Non-universal Critical Quantities from Variational Perturbation Theory and Their Application to the BEC Temperature Shift
For an O(N) symmetric scalar field theory with Euclidean action integral d^3x
[1/2 |nabla phi|^2 + 1/2 r phi^2 + 1/4! u phi^4], where phi = (phi_1,...,phi_N)
is a vector of N real field components, variational perturbation theory through
seven loops is employed for N = 0,1,2,3,4 to compute the renormalized value of
r/(N+2)u^2 at the phase transition. Its exact large-N limit is determined as
well. We also extend an earlier computation of the interaction-induced shift
Delta/Nu for N = 1,2,4 to N = 0,3. For N = 2, the results for the two
quantities are used to compute the second-order shift of the condensation
temperature of a dilute Bose gas, both in the homogenous case and for the wide
limit of a harmonic trap. Our results are in agreement with earlier Monte Carlo
simulations for N = 1,2,4. The appendix contains previously unpublished
numerical seven-loop data provided to us by B.Nickel.Comment: 19 page
Simplified Transfer Matrix Approach in the Two-Dimensional Ising Model with Various Boundary Conditions
A recent simplified transfer matrix solution of the two-dimensional Ising
model on a square lattice with periodic boundary conditions is generalized to
periodic-antiperiodic, antiperiodic-periodic and antiperiodic-antiperiodic
boundary conditions. It is suggested to employ linear combinations of the
resulting partition functions to investigate finite-size scaling. An exact
relation of such a combination to the partition function corresponding to
Brascamp-Kunz boundary conditions is found.Comment: Phys.Rev.E, to be publishe
Recursive Graphical Construction of Feynman Diagrams in phi^4 Theory: Asymmetric Case and Effective Energy
The free energy of a multi-component scalar field theory is considered as a
functional W[G,J] of the free correlation function G and an external current J.
It obeys non-linear functional differential equations which are turned into
recursion relations for the connected Greens functions in a loop expansion.
These relations amount to a simple proof that W[G,J] generates only connected
graphs and can be used to find all such graphs with their combinatoric weights.
A Legendre transformation with respect to the external current converts the
functional differential equations for the free energy into those for the
effective energy Gamma[G,Phi], which is considered as a functional of the free
correlation function G and the field expectation Phi. These equations are
turned into recursion relations for the one-particle irreducible Greens
functions. These relations amount to a simple proof that Gamma[G,J] generates
only one-particle irreducible graphs and can be used to find all such graphs
with their combinatoric weights. The techniques used also allow for a
systematic investigation into resummations of classes of graphs. Examples are
given for resumming one-loop and multi-loop tadpoles, both through all orders
of perturbation theory. Since the functional differential equations derived are
non-perturbative, they constitute also a convenient starting point for other
expansions than those in numbers of loops or powers of coupling constants. We
work with general interactions through four powers in the field.Comment: 34 pages; abstract expanded; section IV.E about absorption of
tadpoles and one related reference added; eqs. (20) and (23) corrected;
further references added; some minor beautifications; to be published by
Phys.Rev.
Five-Loop Vacuum Energy Beta Function in phi^4 Theory with O(N)-Symmetric and Cubic Interactions
The beta function of the vacuum energy density is analytically computed at
the five-loop level in O(N)-symmetric phi^4 theory, using dimensional
regularization in conjunction with the MSbar scheme. The result for the case of
a cubic anisotropy is also given. It is pointed out how to also obtain the beta
function of the coupling and the gamma function of the mass from vacuum graphs.
This method may be easier than traditional approaches.Comment: 16 pages, LaTeX; "note added" fixe
Two-Loop Effective Potential of O(N)-Symmetric Scalar QED in 4-epsilon Dimensions
The effective potential of scalar QED is computed analytically up to two
loops in the Landau gauge. The result is given in 4-epsilon dimensions using
minimal subtraction and epsilon-expansions. In three dimensions, our
calculation is intended to help throw light on unsolved problems of the
superconducting phase transition, where critical exponents and the position of
the tricritical point have not yet found a satisfactory explanation within the
renormalization group approach.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper (including all PS fonts) at
http://www.physik.fu-berlin.de/~kleinert/32
Renormalization Group Summation and the Free Energy of Hot QCD
Using an approach developed in the context of zero-temperature QCD to
systematically sum higher order effects whose form is fixed by the
renormalization group equation, we sum to all orders the leading log (LL) and
next-to-leading log (NLL) contributions to the thermodynamic free energy in hot
QCD. While the result varies considerably less with changes in the
renormalization scale than does the purely perturbative result, a novel
ambiguity arises which reflects the strong scheme dependence of thermal
perturbation theory.Comment: 7 pages REVTEX4, 2 figures; v2: typos correcte
Optimal trap shape for a Bose gas with attractive interactions
Dilute Bose gas with attractive interactions is considered at zero
temperature, when practically all atoms are in Bose-Einstein condensate. The
problem is addressed aiming at answering the question: What is the optimal trap
shape allowing for the condensation of the maximal number of atoms with
negative scattering lengths? Simple and accurate analytical formulas are
derived allowing for an easy analysis of the optimal trap shapes. These
analytical formulas are the main result of the paper.Comment: Latex file, 21 page
Sphalerons with CP-Violating Higgs Potentials
We investigate the effect on the sphaleron in the two Higgs doublet
electroweak theory of including CP violation in the Higgs potential. To have
better control over the relation between the sphaleron energy and the physical
quantities in the theory, we show how to parametrize the Higgs potential in
terms of physical masses and mixing angles, one of which causes CP violation.
By altering this CP violating angle (and keeping the other physical quantities
fixed) the sphaleron energy increases by up to 10%. We also calculate the
static minimum energy path between adjacent vacua as a function of Chern-Simons
number, using the method of gradient flow. The only effect CP violation has on
the barrier is the change in height. As a by-product of our work on
parametrization of the potential, we demonstrate that CP violation in the Higgs
sector favours nearly degenerate light Higgs masses.Comment: 13pp LaTeX2e, 2 eps figs, uses graphicx, a
Mass Expansions of Screened Perturbation Theory
The thermodynamics of massless phi^4-theory is studied within screened
perturbation theory (SPT). In this method the perturbative expansion is
reorganized by adding and subtracting a mass term in the Lagrangian. We
analytically calculate the pressure and entropy to three-loop order and the
screening mass to two-loop order, expanding in powers of m/T. The truncated
m/T-expansion results are compared with numerical SPT results for the pressure,
entropy and screening mass which are accurate to all orders in m/T. It is shown
that the m/T-expansion converges quickly and provides an accurate description
of the thermodynamic functions for large values of the coupling constant.Comment: 22 pages, 10 figure
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