6,675 research outputs found
The Phase Diagram of Scalar Field Theory on the Fuzzy Disc
Using a recently developed bootstrapping method, we compute the phase diagram
of scalar field theory on the fuzzy disc with quartic even potential. We find
three distinct phases with second and third order phase transitions between
them. In particular, we find that the second order phase transition happens
approximately at a fixed ratio of the two coupling constants defining the
potential. We compute this ratio analytically in the limit of large coupling
constants. Our results qualitatively agree with previously obtained numerical
results.Comment: 1+17 pages, v2: typos fixed, published versio
Trefftz Difference Schemes on Irregular Stencils
The recently developed Flexible Local Approximation MEthod (FLAME) produces
accurate difference schemes by replacing the usual Taylor expansion with
Trefftz functions -- local solutions of the underlying differential equation.
This paper advances and casts in a general form a significant modification of
FLAME proposed recently by Pinheiro & Webb: a least-squares fit instead of the
exact match of the approximate solution at the stencil nodes. As a consequence
of that, FLAME schemes can now be generated on irregular stencils with the
number of nodes substantially greater than the number of approximating
functions. The accuracy of the method is preserved but its robustness is
improved. For demonstration, the paper presents a number of numerical examples
in 2D and 3D: electrostatic (magnetostatic) particle interactions, scattering
of electromagnetic (acoustic) waves, and wave propagation in a photonic
crystal. The examples explore the role of the grid and stencil size, of the
number of approximating functions, and of the irregularity of the stencils.Comment: 28 pages, 12 figures; to be published in J Comp Phy
Lie 2-algebra models
In this paper, we begin the study of zero-dimensional field theories with
fields taking values in a semistrict Lie 2-algebra. These theories contain the
IKKT matrix model and various M-brane related models as special cases. They
feature solutions that can be interpreted as quantized 2-plectic manifolds. In
particular, we find solutions corresponding to quantizations of R^3, S^3 and a
five-dimensional Hpp-wave. Moreover, by expanding a certain class of Lie
2-algebra models around the solution corresponding to quantized R^3, we obtain
higher BF-theory on this quantized space.Comment: 47 pages, presentation improved, version published in JHE
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