相关论文: From Percolation to Logarithmic Conformal Field Th…

Using conformal field theory, we derive several new crossing formulas at the two-dimensional percolation point. High-precision simulation confirms these results. Integrating them gives a unified derivation of Cardy's formula for the…

The logarithmic conformal field theory describing critical percolation is further explored using Watts' determination of the probability that there exists a cluster connecting both horizontal and vertical edges. The boundary condition…

These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…

The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…

Logarithmic operators and logarithmic conformal field theories are reviewed. Prominent examples considered here include c=-2 and c=0 logarithmic conformal field theories. c=0 logarithmic conformal field theories are especially interesting…

Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our…

This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with a pure Virasoro example, critical percolation, then continues with a detailed exposition of symplectic fermions,…

We consider the three new crossing probabilities for percolation recently found via conformal field theory by Simmons, Kleban and Ziff. We prove that all three of them (i) may be simply expressed in terms of Cardy's and Watts' crossing…

The local logarithmic conformal field theory corresponding to the triplet algebra at c=-2 is constructed. The constraints of locality and crossing symmetry are explored in detail, and a consistent set of amplitudes is found. The spectrum of…

We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two-- and three-- point functions. This calculation is done for the general case of more than one…

We construct logarithmic conformal field theories starting from an ordinary conformal field theory -- with a chiral algebra C and the corresponding space of states V -- via a two-step construction: i) deforming the chiral algebra…

We examine crossing probabilities and free energies for conformally invariant critical 2-D systems in rectangular geometries, derived via conformal field theory and Stochastic L\"owner Evolution methods. These quantities are shown to…

We find the fusion rules for the c_{p,1} series of logarithmic conformal field theories. This completes our attempts to generalize the concept of rationality for conformal field theories to the logarithmic case. A novelty is the appearance…

Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…

We describe an approach to logarithmic conformal field theories as limits of sequences of ordinary conformal field theories with varying central charge c. Logarithmic behaviour arises from degeneracies in the spectrum of scaling dimensions…

A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…

It is discussed how a limiting procedure of (super)conformal field theories may result in logarithmic (super)conformal field theories. The construction is illustrated by logarithmic limits of (unitary) minimal models in conformal field…

A solution to the long-standing problem of identifying the conformal field theory governing the transition between quantized Hall plateaus of a disordered noninteracting 2d electron gas, is proposed. The theory is a nonlinear sigma model…

We discuss the effect of boundaries in boundary logarithmic conformal field theory and show, with reference to both $c=-2$ and $c=0$ models, how they produce new features even in bulk correlation functions which are not present in the…

We study the logarithmic conformal field theories in which conformal weights are continuous subset of real numbers. A general relation between the correlators consisting of logarithmic fields and those consisting of ordinary conformal…