24 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.
Hitting all Maximal Independent Sets of a Bipartite Graph
We prove that given a bipartite graph G with vertex set V and an integer k,
deciding whether there exists a subset of V of size k hitting all maximal
independent sets of G is complete for the class Sigma_2^P.Comment: v3: minor chang
c-function and central charge of the sine-Gordon model from the non-perturbative renormalization group flow
In this paper we study the c-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the c-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency \u3b22, where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points (\u3b22<8\u3c0) to the infra-red limit is in good quantitative agreement with the expected \u3b4c=1 result. The behavior of the c-function in the other parts of the flow diagram is also discussed. Finally, we point out that including also higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account. Rather, incorporating the wave-function renormalization (i.e. going beyond local potential approximation) is crucial to get sensible results even when a single frequency is used
The nonperturbative functional renormalization group and its applications
The renormalization group plays an essential role in many areas of physics,
both conceptually and as a practical tool to determine the long-distance
low-energy properties of many systems on the one hand and on the other hand
search for viable ultraviolet completions in fundamental physics. It provides
us with a natural framework to study theoretical models where degrees of
freedom are correlated over long distances and that may exhibit very distinct
behavior on different energy scales. The nonperturbative functional
renormalization-group (FRG) approach is a modern implementation of Wilson's RG,
which allows one to set up nonperturbative approximation schemes that go beyond
the standard perturbative RG approaches. The FRG is based on an exact
functional flow equation of a coarse-grained effective action (or Gibbs free
energy in the language of statistical mechanics). We review the main
approximation schemes that are commonly used to solve this flow equation and
discuss applications in equilibrium and out-of-equilibrium statistical physics,
quantum many-particle systems, high-energy physics and quantum gravity.Comment: v2) Review article, 93 pages + bibliography, 35 figure
On the upper chromatic number and multiple blocking sets of PG(n,q)
We investigate the upper chromatic number of the hypergraph formed by the
points and the -dimensional subspaces of ; that is, the
most number of colors that can be used to color the points so that every
-subspace contains at least two points of the same color. Clearly, if one
colors the points of a double blocking set with the same color, the rest of the
points may get mutually distinct colors. This gives a trivial lower bound, and
we prove that it is sharp in many cases. Due to this relation with double
blocking sets, we also prove that for , a small -fold
(weighted) -blocking set of , prime, must contain
the weighted sum of not necessarily distinct -spaces.Comment: 21 page