Related papers: Comment on `Series expansions from the corner tran…
We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum -- and, in particular, classical -- interactions. Our approach is based on the use of ``decoupling parameters", advocated by Park [34], which…
In this article, we have studied transformation formulas of zeta function at odd integers over an arbitrary number field which in turn generalizes Ramanujan's identity for the Riemann zeta function. The above transformation leads to a new…
We present a construction of $\kappa$-deformed complex scalar field theory with the objective of shedding light on the way discrete symmetries and CPT invariance are affected by the deformation. Our starting point is the observation that,…
A generalization of the regular continued fractions was given by Chakraborty and Rao \cite{CR-2003}. For the transformation which generates this expansion and its invariant measure, the Perron-Frobenius operator is given and studied. For…
In this work we show that the Riemann hypothesis for the Dedekind zeta--function $\zeta_{\mathrm{K}}(s)$ of an algebraic number field $\mathrm{K}$ is equivalent to a problem of the rate of convergence of certain discrete measures defined…
We develop a formalism for performing real space renormalization group transformations of the "decimation type" using low temperature perturbation theory. This type of transformations beyond $d=1$ is highly nontrivial even for free…
Starting from Wilson's action, we calculate strong coupling series for the Polyakov loop susceptibility in lattice gauge theories for various small N_\tau in the thermodynamic limit. Analysing the series with Pad\'e approximants, we…
We study the analyticity of the partition function of the hard hexagon model in the complex fugacity plane by computing zeros and transfer matrix eigenvalues for large finite size systems. We find that the partition function per site…
It is shown by the method of renormalized field theory that in contrast to a statement based on a mathematically ill-defined invariance transformation and found in most of the recent publications on growth models with surface diffusion, the…
The paper presents fundamental metrical theorems for a class of continued fraction-like expansions known as $\theta$-expansions. We first prove Khinchine's Weak Law of Large Numbers for the sum of digits, followed by the Diamond-Vaaler…
Salmhofer [Commun. Math. Phys. 194, 249 (1998)] has recently developed a new renormalization group method for interacting Fermi systems, where the complete flow from the bare action of a microscopic model to the effective low-energy action,…
A strong-coupling expansion for the phase boundary of the (incompressible) Mott insulator is presented for the bose Hubbard model. Both the pure case and the disordered case are examined. Extrapolations of the series expansions provide…
We have reinvestigated the quintessence model with minimally coupled scalar field in the context of recent Supernova observation at $z=1.7$. By assuming the form of the scale factor which gives both the early time deceleration and late time…
We argue that the torus partition sum in $2d$ (super) gravity, which counts physical states in the theory, is a decreasing function of the renormalization group scale. As an application we chart the space of $(\hat c\leq1)$ $c\leq1$ models…
After recalling the precise existence conditions of the zeta function of a pseudodifferential operator, and the concept of reflection formula, an exponentially convergent expression for the analytic continuation of a multidimensional…
We make an analysis of the two-dimensional U(1) lattice gauge theory with a $\theta$ term by using the tensor renormalization group. Our numerical result for the free energy shows good consistency with the exact one at finite coupling…
We develop, based on Baxter's corner transfer matrices, a renormalizable numerically exact method for computation of the level density of the quasi-energy spectra of two-dimensional (2D) locally interacting many-body Floquet systems. We…
Let p be a prime. For any finite p-group G, the deep transfers T(H,G'):H/H' --> G'/G'' from the maximal subgroups H of index (G:H)=p in G to the derived subgroup G' are introduced as an innovative tool for identifying G uniquely by means of…
We calculate the critical exponent $\eta$ of the $D$-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction. Our approach relies on the…
We discuss the use of Kaniadakis' $\kappa$-exponential in the construction of a statistical manifold modelled on Lebesgue spaces of real random variables. Some algebraic features of the deformed exponential models are considered. A chart is…