1,641,798 research outputs found
Berezinskii-Kosterlitz-Thouless transition and criticality of an elliptic deformation of the sine-Gordon model
We introduce and study the properties of a periodic model interpolating
between the sine-- and the sinh--Gordon theories in dimensions. This
model shows the peculiarities, due to the preservation of the functional form
of their potential across RG flows, of the two limiting cases: the sine-Gordon,
not having conventional order/magnetization at finite temperature, but
exhibiting Berezinskii-Kosterlitz-Thouless (BKT) transition; and the
sinh-Gordon, not having a phase transition, but being integrable. The
considered interpolation, which we term as {\em sn-Gordon} model, is performed
with potentials written in terms of Jacobi functions. The critical properties
of the sn-Gordon theory are discussed by a renormalization-group approach. The
critical points, except the sinh-Gordon one, are found to be of BKT type.
Explicit expressions for the critical coupling as a function of the elliptic
modulus are given.Comment: v2, 10 pages, 8 figures, accepted in J. Phys.
On non commutative sinh-Gordon Equation
We give a noncommutative extension of sinh-Gordon equation. We generalize a
linear system and Lax representation of the sinh-Gordon equation in
noncommutative space. This generalization gives a noncommutative version of the
sinh-Gordon equation with extra constraints, which can be expressed as global
conserved currents.Comment: 7 Page
Quantization of Solitons and the Restricted Sine-Gordon Model
We show how to compute form factors, matrix elements of local fields, in the
restricted sine-Gordon model, at the reflectionless points, by quantizing
solitons. We introduce (quantum) separated variables in which the Hamiltonians
are expressed in terms of (quantum) tau-functions. We explicitly describe the
soliton wave functions, and we explain how the restriction is related to an
unusual hermitian structure. We also present a semi-classical analysis which
enlightens the fact that the restricted sine-Gordon model corresponds to an
analytical continuation of the sine-Gordon model, intermediate between
sine-Gordon and KdV.Comment: 29 pages, Latex, minor updatin
Study of models of the sine-Gordon type in flat and curved spacetime
We study a new family of models of the sine-Gordon type, starting from the
sine-Gordon model, including the double sine-Gordon, the triple one, and so on.
The models appears as deformations of the starting model, with the deformation
controlled by two parameters, one very small, used to control a linear
expansion on it, and the other, which specifies the particular model in the
family of models. We investigate the presence of topological defects, showing
how the solutions can be constructed explicitly from the topological defects of
the sine-Gordon model itself. In particular, we delve into the double
sine-Gordon model in a braneworld scenario with a single extra dimension of
infinite extent, showing that a stable gravity scenario is admissible. Also, we
briefly show that the deformation procedure can be used iteratively, leading to
a diversity of possibilities to construct families of models of the sine-Gordon
type.Comment: 8 pages, 7 figures; Title changed, author and new results included;
version to appear in EPJ
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