Renormalization group theory of the generalized multi-vertex sine-Gordon model

We investigate the renormalization group theory of the generalized multi-vertex sine-Gordon model by employing the dimensional regularization method and also the Wilson renormalization group method. The vertex interaction is given by $\cos(k_j\cdot \phi)$, where $k_j$ ($j=1,2,\ldots,M$) are momentum vectors and $\phi$ is an $N$-component scalar field. The beta functions are calculated for the sine-Gordon model with multiple cosine interactions. The second-order correction in the renormalization procedure is given by the two-point scattering amplitude for tachyon scattering. We show that new vertex interaction with the momentum vector $k_{\ell}$ is generated from two vertex interactions with vectors $k_i$ and $k_j$ when $k_i$ and $k_j$ meet the condition $k_{\ell}=k_i\pm k_j$, called the triangle condition. A further condition $k_i\cdot k_j=\pm 1/2$ is required within the dimensional regularization method. The renormalization group equations form a set of closed equations when $\{k_j\}$ form an equilateral triangle for $N=2$ or a regular tetrahedron for $N=3$. The Wilsonian renormalization group method gives qualitatively the same result for beta functions.

Critical Site Percolation in High Dimension

We use the lace expansion to prove an infra-red bound for site percolation on the hypercubic lattice in high dimension. This implies the triangle condition and allows us to derive several critical exponents that characterize mean-field behavior in high dimensions.

The Cressey hypothesis (1953) and an investigation into the occurrence of corporate fraud: an empirical analysis conducted in Brazilian banking institutions

ABSTRACT This article fills a technical-scientific gap that currently exists in the Brazilian literature on corporative fraud, by combining the theoretical framework of agency theory, of criminology, and of the economics of crime. In addition, it focuses on a sector that is usually excluded from analyses due to its specific characteristics and shows the application of multinomial logit panel data regression with random effects, which is rarely used in studies in the area of accounting. The aim of this study is to investigate the occurrence of corporative fraud, as well as cases of fraud in Brazilian banking institutions, by using detection variables related to the Cressey fraud triangle. Research into fraud and methods of detecting fraud has grown in management literature, especially after the occurrence of various corporative scandals in the 1990s. Although regulatory agencies have increased their investments in monitoring and control, fraud investigations and convictions are still common in the day-to-day administration of banks, as can be seen in the Brazilian Central Bank and the National Financial System Resource Council’s databases of punitive proceedings. We believe that this article will have a positive impact in the area of accounting sciences, since it involves corporative fraud in a multidisciplinary form and because it provides the incentive to use a quantitative tool that can help increase the development of similar studies in the area. This study tested the theory that the dimensions of the fraud triangle condition the occurrence of corporative fraud in Brazilian banking institutions. Thirty-two representative variables of corporative fraud were identified in the theoretical-empirical review, which were reduced to seven latent variables by the principal component analysis. Finally, the seven factors formed the independent variables in the multinomial logit models used in the hypothesis tests, which presented promising results.