General solution of an exact correlation function factorization in conformal field theory (2009)
Simmons, Jacob J. H., Kleban, Peter
We discuss a correlation function factorization, which relates a three-point function to the square root of three two-point functions. This factorization is known to hold for certain scaling...
New percolation crossing formulas and second-order modular forms (2009)
Diamantis, Nikolaos, Kleban, Peter
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...
Simmons, J. J. H., Ziff, Robert M., Kleban, Peter
We consider the density at a point z = x + i y of critical percolation clusters that touch the left [P_L(z)], right [P_R(z)], or both [P_{LR}(z)] sides of a rectangular system, with open boundary...
First Column Boundary Operator Product Expansion Coefficients (2007)
Simmons, Jacob J. H., Kleban, Peter
We calculate boundary operator product expansion coefficients for boundary operators in the first column of the Kac table in conformal field theories. For c=0 we give closed form expressions for all...
FAST TRACK COMMUNICATION: Percolation crossing formulae and conformal field theory (2007)
Simmons, Jacob J H, Kleban, Peter, Ziff, Robert M
Using conformal field theory, we derive several new crossing formulae at the two-dimensional percolation point. High-precision simulation confirms these results. Integrating them gives a unified...
Exact factorization of correlation functions in 2-D critical percolation (2007)
Simmons, Jacob J. H., Kleban, Peter, Ziff, Robert M.
By use of conformal field theory, we discover several exact factorizations of higher-order density correlation functions in critical two-dimensional percolation. Our formulas are valid in the upper...
The density of critical percolation clusters touching the boundaries of strips and squares (2007)
Simmons, Jacob J H, Kleban, Peter, Dahlberg, Kevin, Ziff, Robert M
We consider the density of two-dimensional critical percolation clusters, constrained to touch one or both boundaries, in infinite strips, half-infinite strips and squares, as well as several related...
Percolation Crossing Formulas and Conformal Field Theory (2007)
Simmons, Jacob J. H., Kleban, Peter, Ziff, Robert M.
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...
The density of critical percolation clusters touching the boundaries of strips and squares (2007)
Simmons, Jacob J. H., Kleban, Peter, Dahlberg, Kevin, Ziff, Robert M.
We consider the density of two-dimensional critical percolation clusters, constrained to touch one or both boundaries, in infinite strips, half-infinite strips, and squares, as well as several...
Intervals Between Farey Fractions in the Limit of Infinite Level (2005)
The modified Farey sequence consists, at each level k, of rational fractions r_k^(n), with n=1, 2, ...,2^k+1. We consider I_k^(e), the total length of (one set of) alternate intervals between Farey...
We generalize the number theoretic spin chain, a one-dimensional statistical model based on the Farey fractions, by introducing a new parameter x>=0. This allows us to write recursion relations in...
We present a systematic procedure for the direct calculation of the free energy and its first and second derivatives for the Ising model in one to three dimensions with a wide class of symmetry...
Thermodynamics of the Farey Fraction Spin Chain (2003)
We consider the Farey fraction spin chain, a one-dimensional model defined on (the matrices generating) the Farey fractions. We extend previous work on the thermodynamics of this model by introducing...
Crossing Probabilities and Modular Forms (2002)
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...
The Phase Transition in Statistical Models Defined on Farey Fractions (2002)
Fiala, Jan, Kleban, Peter, Ozluk, Ali
We consider several statistical models defined on the Farey fractions. Two of these models may be regarded as "spin chains", with long-range interactions, while another arises in the study of...
Crossing Probabilities in Critical 2-D Percolation and Modular Forms (1999)
Crossing probabilities for critical 2-D percolation on large but finite lattices have been derived via boundary conformal field theory. These predictions agree very well with numerical results....
A Fully Magnetizing Phase Transition (1998)
Contucci, Pierluigi, Kleban, Peter, Knauf, Andreas
We analyze the Farey spin chain, a one dimensional spin system with effective interaction decaying like the squared inverse distance. Using a polymer model technique, we show that when the...
Shape-dependent universality in percolation (1998)
Ziff, Robert M., Lorenz, Christian D., Kleban, Peter
The shape-dependent universality of the excess percolation cluster number and cross-configuration probability on a torus is discussed. Besides the aspect ratio of the torus, the universality class...
Phase Diagram of Ising Models with Random Sublattice Vacancies. (1998)
We use a modified Kadanoff's variational method to calculate the phase diagram of an Ising model with random vacancies on one of two interpenetrating sublattices of the isotropic square (SQ) and...
A Fully Magnetizing Phase Transition (1998)
Pierluigi Contucci, Peter Kleban, Andreas Knauf
We analyze the Farey spin chain, a one dimensional spin system with effective interaction decaying like the squared inverse distance. Using a polymer model technique, we show that when the...
A Fully Magnetizing Phase Transition (1998)
Peter Klebau, Pierluigi Contucci, Pierluigi Contucci, Peter Kleban, Andreas Knauf, Andreas Knauf
We analyze the Farey spin chain, a one dimensional spin system with effective interaction decaying like the squared inverse distance. Using a polymer model technique, we show that when the...
Casimir Terms and Shape Instabilities for Two-Dimensional Critical Systems (1996)
We calculate the universal part of the free energy of certain finite two- dimensional regions at criticality by use of conformal field theory. Two geometries are considered: a section of a circle...
Chaos and parametric management
Wilson, James A, Acheson, James, Kleban, Peter
A number of people provided helpful comments and suggestions during the preparation of this reply. None of them, of course, bear responsibility for any mistakes or conclusions drawn here. They were:...