Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions

We present an analytic study of the Potts model partition function on two different types of self-similar lattices of triangular shape with non integer Hausdorff dimension. Both types of lattices analyzed here are interesting examples of non-trivial thermodynamics in less than two dimensions. First, the Sierpinski gasket is considered. It is shown that, by introducing suitable geometric coefficients, it is possible to reduce the computation of the partition function to a dynamical system, whose variables are directly connected to (the arising of) frustration on macroscopic scales, and to determine the possible phases of the system. The same method is then used to analyse the Hanoi graph. Again, dynamical system theory provides a very elegant way to determine the phase diagram of the system. Then, exploiting the analysis of the basins of attractions of the corresponding dynamical systems, we construct various examples of self-similar lattices with more than one critical temperature. These multiple critical temperatures correspond to crossing phases with different degrees of frustration.Comment: 16 pages, 12 figures, 1 table; title changed, references and discussion on multiple transitions adde

Local supersymmetry without SUSY partners

A gauge theory for a superalgebra that includes an internal gauge (G) and local Lorentz algebras, and that could describe the low energy particle phenomenology is constructed. These two symmetries are connected by fermionic supercharges. The system includes an internal gauge connection 1-form $A$, a spin-1/2 Dirac spinor $\psi$, the Lorentz connection $\omega$, and the vielbein $e$. The connection one-form is in the adjoint representation of G, while $\psi$ is in the fundamental. In contrast to standard supergravity, the metric is not a fundamental field and is in the center of the superalgebra: it is not only invariant under the internal gauge group and under Lorentz transformations, but is also invariant under supersymmetry. The features of this theory that mark the difference with standard supersymmetry are: A) The number of fermionic and bosonic states is not necessarily the same; B) There are no superpartners with equal mass, "bosoninos", sleptons and squarks are absent; C) Although this supersymmetry originates in a local gauge theory and gravity is included, there is no gravitino; D) Fermions acquire mass from their coupling to the background or from self-couplings, while bosons remain massless. In odd dimensions, the Chern-Simons form provides an action that is quasi-invariant under the entire superalgebra. In even dimensions, the Yang-Mills form $$ is the only natural option, and the symmetry breaks down to [G x SO(1,D-1)]. In 4D, the construction follows the Townsend - Mac Dowell-Mansouri approach. Due to the absence of osp(4|2)-invariant traces in four dimensions, the resulting Lagrangian is only invariant under [U(1) x SO(3,1)], and includes a Nambu--Jona-Lasinio term. In this case, the Lagrangian depends on a single dimensionful parameter that fixes Newton's constant, the cosmological constant and the NJL coupling.Comment: 24 pages, no figures. Title changed in journal version to "Unconventional supersymmetry and its breaking". Few references added and some paragraphs rewritten from v.1. This version includes two appendices that are not found in the journal versio

Exact partition function of the Potts model on the Sierpinski gasket and the Hanoi lattice

We present an analytic study of the Potts model partition function on the Sierpinski and Hanoi lattices, which are self-similar lattices of triangular shape with non integer Hausdorff dimension. Both lattices are examples of non-trivial thermodynamics in less than two dimensions, where mean field theory does not apply. We used and explain a method based on ideas of graph theory and renormalization group theory to derive exact equations for appropriate variables that are similar to the restricted partition functions. We benchmark our method with Metropolis Monte Carlo simulations. The analysis of fixed points reveals information of location of the Fisher zeros and we provide a conjecture about the location of zeros in terms of the boundary of the basins of attraction.Comment: 35 pages, 13 figures. arXiv admin note: substantial text overlap with arXiv:1007.408

The BTZ black hole as a Lorentz-flat geometry

It is shown that 2+1 dimensional anti-de Sitter spacetimes are Lorentz-flat. This means, in particular, that any simply-connected patch of the BTZ black hole solution can be endowed with a Lorentz connection that is locally pure gauge. The result can be naturally extended to a wider class of black hole geometries and point particles in three-dimensional spacetime.Comment: 2 page

Expression of a novel versican variant in dorsal root ganglia from spared nerve injury rats

The size and modular structure of versican and its gene suggest the existence of multiple splice variants. We have identified, cloned, and sequenced a previously unknown exon located within the noncoding gene sequence downstream of exon 8. This exon, which we have named exon 8β, specifies two stop-codons. mRNAs of the versican gene with exon 8β are predicted to be constitutively degraded by nonsense-mediated RNA decay. Here, we tested the hypothesis that these transcripts become expressed in a model of neuropathic pain