Related papers: The Yang-Lee Edge Singularity and Related Problems
The conditions leading to a nontrivial renormalization of the topological charge in four--dimensional Yang--Mills theory are discussed. It is shown that if the topological term is regarded as the limit of a certain nontopological…
We study a discretization of ${\cal N}=2$ super Yang-Mills theory which possesses a single exact supersymmetry at non-zero lattice spacing. This supersymmetry arises after a reformulation of the theory in terms of {\it twisted} fields. In…
One of the simplest examples of a PT-symmetric quantum system is the scaling Yang-Lee model, a quantum field theory with cubic interaction and purely imaginary coupling. We give a historical review of some facts about this model in d <= 2…
A recent investigation of SU(2) Yang-Mills theory found several classical solutions with bad behaviour at infinity : one of the potential components oscillated and another tended to infinity. In this paper we apply an idea due to Heisenberg…
We use the effective potential method to study the $\mathcal{PT}$-symmetry breaking of the non-Hermitian $i\phi^{3}$ field theory in $6-\epsilon$ space-time dimensions. The critical exponents so obtained coincide with the exact values…
The influence of long-range interactions decaying in d dimensions as 1/R^{d+\sigma} on the critical behavior of systems with Fisher's correlation-function exponent for short-range interactions \eta_{SR}<0, is re-examined. Such systems,…
Yang-Mills tree-level amplitudes contain singularities of codimension one like collinear and multi-particle factorizations, codimension two such as soft limits, as well as higher codimension singularities. Traditionally, BCFW-like…
In these lectures I discuss peculiarities of the critical behaviour of ``non-ideal'' systems as it is explained by the renormalization group approach. Examples considered here include account of the single-ion anisotropy, structural…
The Lee-Yang circle theorem revolutionized our understanding of phase transitions in ferromagnetic systems by showing that the complex zeros of partition functions lie on the unit circle, with criticality arising as these zeros approach the…
Chen-Ning Yang made important contributions to the theory of solvable models in statistical mechanics, including generalizations of the Bethe Ansatz, magnetization in the Ising model, the Lee-Yang circle theorem, and the Yang-Baxter…
The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of…
We consider renormalization of effective field theory interactions by discretizing the continuum on a tight-binding lattice. After studying the one-dimensional problem, we address s-wave collisions in three dimensions and relate the bare…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…
We study the Borel-Pad\'e resummation of the asymptotic series for the string equation of the Lee-Yang edge singularity. Numerical methods are provided to compute a high accuracy exact solution. We find the resummation matches the numerical…
Using the electrostatic analogy, we derive an exact formula for the limiting Yang-Lee zero distribution in the random allocation model of general weights. This exhibits a real-space condensation phase transition, which is induced by 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…
A gauge invariant regularisation for dealing with pure Yang-Mills theories within the exact renormalization group approach is proposed. It is based on the regularisation via covariant higher derivatives and includes auxiliary Pauli-Villars…
We show how to obtain the critical exponent of magnetization in the Lee-Yang edge singularity model coupled to two-dimensional quantum gravity.
We study the Quantum Chromodynamics (QCD) phase transitions in the complex chemical potential plane in the framework of Dyson-Schwinger equation approach, in the presence of a constant gluonic background field that represents confining…
In this letter, the integrability aspects of a generalized Fisher type equation with modified diffusion in (1+1) and (2+1) dimensions are studied by carrying out a singularity structure and symmetry analysis. It is shown that the Painlev\'e…