14,695 research outputs found
On the boundary Ising model with disorder operators
We extend the well-known method of calculating bulk correlation functions of
the conformal Ising model via bosonisation to situations with boundaries.
Oshikawa and Affleck have found the boundary states of two decoupled Ising
models in terms of the orbifold of a single free boson compactified on a circle
of radius r=1; we adapt their results to include disorder operators. Using
these boundary states we calculate the expectation value of a single disorder
field on a cylinder with free boundary conditions and show that in the
appropriate limits we recover the standard and frustrated partition functions.
We also show how to calculate Ising correlation functions on the upper half
plane.Comment: 12 pages, Latex2e, 6 figure
A non-rational CFT with c=1 as a limit of minimal models
We investigate the limit of minimal model conformal field theories where the
central charge approaches one. We conjecture that this limit is described by a
non-rational CFT of central charge one. The limiting theory is different from
the free boson but bears some resemblance to Liouville theory. Explicit
expressions for the three point functions of bulk fields are presented, as well
as a set of conformal boundary states. We provide analytic and numerical
arguments in support of the claim that this data forms a consistent CFT.Comment: latex2e, 37 pages, 4 figure
On the relation between Phi(1,2) and Phi(1,5) perturbed minimal models
We consider the RSOS S-matrices of the Phi(1,5) perturbed minimal models
which have recently been found in the companion paper [hep-th/9604098]. These
S-matrices have some interesting properties, in particular, unitarity may be
broken in a stronger sense than seen before, while one of the three classes of
Phi(1,5) perturbations (to be described) shares the same Thermodynamic Bethe
Ansatz as a related Phi(1,2) perturbation. We test these new S-matrices by the
standard Truncated Conformal Space method, and further observe that in some
cases the BA equations for two particle energy levels may be continued to
complex rapidity to describe (a) single particle excitations and (b) complex
eigenvalues of the Hamiltonian corresponding to non-unitary S-matrix elements.
We make some comments on identities between characters in the two related
models following from the fact that the two perturbed theories share the same
breather sector.Comment: LaTeX, 23 pages, 12 figures. Substantial revision of introductory
section, new discussion of complex eigenvalues and non-unitary S-matrice
Finite size effects in perturbed boundary conformal field theories
We discuss the finite-size properties of a simple integrable quantum field
theory in 1+1 dimensions with non-trivial boundary conditions. Novel
off-critical identities between cylinder partition functions of models with
differing boundary conditions are derived.Comment: 7 pages, 11 figures, JHEP proceedings style. Uses epsfig, amssymb.
Talk given at the conference `Nonperturbative Quantum Effects 2000', Pari
Epidemics and percolation in small-world networks
We study some simple models of disease transmission on small-world networks,
in which either the probability of infection by a disease or the probability of
its transmission is varied, or both. The resulting models display epidemic
behavior when the infection or transmission probability rises above the
threshold for site or bond percolation on the network, and we give exact
solutions for the position of this threshold in a variety of cases. We confirm
our analytic results by numerical simulation.Comment: 6 pages, including 3 postscript figure
A crossing probability for critical percolation in two dimensions
Langlands et al. considered two crossing probabilities, pi_h and pi_{hv}, in
their extensive numerical investigations of critical percolation in two
dimensions. Cardy was able to find the exact form of pi_h by treating it as a
correlation function of boundary operators in the Q goes to 1 limit of the Q
state Potts model. We extend his results to find an analogous formula for
pi_{hv} which compares very well with the numerical results.Comment: 8 pages, Latex2e, 1 figure, uuencoded compressed tar file, (1 typo
changed
- …