Related papers: Potts models on hierarchical lattices and Renormal…
We extend the renormalization group transformation based on the two-lattice matching to the complex inverse temperature plane for Dyson's hierarchical Ising model. We consider values of the dimensional parameter above, below and exactly at…
Recently, several authors have studied maps where a function, describing the local diffusion matrix of a diffusion process with a linear drift towards an attraction point, is mapped into the average of that function with respect to the…
We present rational Lax representations for one-component parametric quadrirational Yang-Baxter maps in both the abelian and non-abelian settings. We show that from the Lax matrices of a general class of non-abelian involutive Yang-Baxter…
We present a solution of the non-linear renormalization group equations leading to the dominant and subdominant singular behaviours of physical quantities (free energy density, correlation length, internal energy, specific heat,…
Real space renormalization group maps, e.g., the majority rule transformation, map Ising type models to Ising type models on a coarser lattice. We show that each coefficient of the renormalized Hamiltonian in the lattice gas variables…
The locations of multicritical points on many hierarchical lattices are numerically investigated by the renormalization group analysis. The results are compared with an analytical conjecture derived by using the duality, the gauge symmetry…
We explicitly compute the critical exponents associated with logarithmic corrections (the so-called hatted exponents) starting from the renormalization group equations and the mean field behavior for a wide class of models at the upper…
We introduce a family of polytope exchange transformations (PETs) acting on parallelotopes in $\R^{2n}$ for $n=1,2,3...$. These PETs are constructed using a pair of lattices in $\R^{2n}$. The moduli space of these PETs is $GL_n(\R)$. We…
This work is concerned with the theory of Graphical Representation for the Ising and Potts Models over general lattices with non-translation invariant external field. We explicitly describe in terms of the Random Cluster Representation the…
We study the critical behavior of the random q-state Potts quantum chain by density matrix renormalization techniques. Critical exponents are calculated by scaling analysis of finite lattice data of short chains ($L \leq 16$) averaging over…
Renormalizations can be considered as building blocks of complex dynamical systems. This phenomenon has been widely studied for iterations of polynomials of one complex variable. Concerning non-polynomial hyperbolic rational maps, a recent…
The Jaynes-Cummings model is a cornerstone of light-matter interactions. While finite, the model provides an illustrative example of renormalisation in perturbation theory. We show, however, that exact renormalisation reveals a rich…
There are reasons to believe that the Standard Model is only an effective theory, with new Physics lying beyond it. Supersymmetric extensions are one possibility: they address some of the Standard Model's shortcomings, such as the…
Renormalization group calculations are used to give exact solutions for rigidity percolation on hierarchical lattices. Algebraic scaling transformations for a simple example in two dimensions produce a transition of second order, with an…
The Yang-Lee zeros of the Q-state Potts model are investigated in 1, 2 and 3 dimensions. Analytical results derived from the transfer matrix for the one-dimensional model reveal a systematic behavior of the locus of zeros as a function of…
We present both analytic and numerical results on the position of the partition function zeros on the complex magnetic field plane of the $q=2$ (Ising) and $q=3$ states Potts model defined on $\phi^3 $ Feynman diagrams (thin random graphs).…
We introduce a new family of tensorial field theories by coupling different fields in a non-trivial way, with a view towards the investigation of the coupling between matter and gravity in the quantum regime. As a first step, we consider…
Lattice regularization is a standard technique for the nonperturbative definition of a quantum theory of fields. Several approaches to the construction of a quantum theory of gravity adopt this technique either explicitly or implicitly. A…
Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate…
While in the fully-connected limit the solution of the spin-glass model is known, with the existence of a complex transition on a critical line in the temperature-external field phase diagram, in finite dimensions we don't know if a…