The taming of recurrences in computability logic through cirquent calculus, Part I

This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of negation, parallel conjunction, parallel disjunction, branching recurrence, and branching corecurrence. The article is published in two parts, with (the present) Part I containing preliminaries and a soundness proof, and (the forthcoming) Part II containing a completeness proof

Renormalization group approach to the one-dimensional 1/4-filled Hubbard model with alternating on-site interactions

The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system and to the dynamical generation of a gap in the charge excitation spectrum for $U_{a}\not=U_{b}$, $U_{a}>0$ or $U_{b}>0$. The ground-state phase diagram is obtained in the limit of second order renormalization. Depending on the sign and relative values of the bare coupling constants, there is a gap in the spin or charge excitation spectrum and the model system tends to superconducting or antiferromagnetic order at T=0, with doubled period. The role of interaction between particles on nearest and next-nearest neighbor sites is also considered

Renormalization of 1S0{}^1S_0 NN scattering amplitude in effective field theory

Cutoff regularized subleading order ${}^1S_0$ NN potential of effective field theory (EFT) is iterated using Lippmann-Schwinger equation. It is shown that the scattering amplitudes calculated in cutoff and subtractively renormalized EFT are equal up to the accuracy of performed calculations. Non-perturbative renormalization, where part of divergences are absorbed into two contact interaction coupling constants with subsequent removal of regularization is also performed. Cutoff and dimensional regularizations both lead to finite but different results within this scheme.Comment: 6 pages, no figures, to be published in Phys. Lett.

Phase Diagram of the spin S=1/2 Extended XY model

The quantum phase transition in the ground state of the Extended spin S=1/2 XY model is studied in detail. Using the exact solution of the model the low temperature thermodynamics, as well as the ground state phase diagram of the model in the presence of applied uniform and/or staggered magnetic field are discussed.Comment: 12 pages, 12 figure

On approximating two distributions from a single complex-valued function

We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function $\psi$ and its Fourier transform. We show that this problem always has a solution within a specified degree of accuracy, provided the distributions satisfy the necessary regularity conditions. We describe the algorithm and construction of $\psi$ and provide examples of approximating several pairs of distributions using the algorithm.Comment: 9 pages, 4 figure

Phase Diagram of the Extended Hubbard Model with Pair Hopping Interaction

A one-dimensional model of interacting electrons with on-site $U$, nearest-neighbor $V$, and pair-hopping interaction $W$ is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin- and charge-density wave phases for large $U$ and $V$, respectively, we identify bond-located ordered phases corresponding to an enhanced Peierls instability in the system for $W<0$, $|U-2V|<|2W|$, and to a staggered magnetization located on bonds between sites for $W>0$, $|U-2V|<W$. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the $\eta_{\pi}$-superconducting phase at $|U-2V| \ll 2t \leq W$ is briefly discussed.Comment: 6 pages in revtex format, 2 fig files in ep

In the beginning was game semantics

This article presents an overview of computability logic -- the game-semantically constructed logic of interactive computational tasks and resources. There is only one non-overview, technical section in it, devoted to a proof of the soundness of affine logic with respect to the semantics of computability logic. A comprehensive online source on the subject can be found at http://www.cis.upenn.edu/~giorgi/cl.htmlComment: To appear in: "Games: Unifying Logic, Language and Philosophy". O. Majer, A.-V. Pietarinen and T. Tulenheimo, eds. Springer Verlag, Berli