Field theory of Ising percolating clusters Gesualdo Delfino
نویسنده
چکیده
The clusters of up spins of a two-dimensional Ising ferromagnet undergo a second order percolative transition at temperatures above the Curie point. We show that in the scaling limit the percolation threshold is described by an integrable field theory and identify the nonperturbative mechanism which allows the percolative transition in absence of thermodynamic singularities. The analysis is extended to the Kertész line along which the Coniglio-Klein droplets percolate in a positive magnetic field.
منابع مشابه
Particle decay in Ising field theory with magnetic field 1 Gesualdo Delfino
The scaling limit of the two-dimensional Ising model in the plane of temperature and magnetic field defines a field theory which provides the simplest illustration of non-trivial phenomena such as spontaneous symmetry breaking and confinement. Here we discuss how Ising field theory also gives the simplest model for particle decay. The decay widths computed in this theory provide the obvious tes...
متن کاملOn the space of quantum fields in massive two-dimensional theories
For a large class of integrable quantum field theories we show that the S-matrix determines a space of fields which decomposes into subspaces labeled, besides the charge and spin indices, by an integer k. For scalar fields k is non-negative and is naturally identified as an off-critical extension of the conformal level. To each particle we associate an operator acting in the space of fields who...
متن کاملIntegrable field theory and critical phenomena . The Ising model in a magnetic field
The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager’s work of the forties, exact results for the magnetic case have been missing until the late eighties, when A. Zamolodchikov solved the model in a field at the critical temperature, di...
متن کاملA Geometrical Interpretation of Hyperscaling Breaking in the Ising Model *
In random percolation one finds that the mean field regime above the upper critical dimension can simply be explained through the coexistence of infinite percolating clusters at the critical point. Because of the mapping between percolation and critical behaviour in the Ising model, one might check whether the breakdown of hyperscaling in the Ising model can also be intepreted as due to an infi...
متن کاملPercolating cluster of center vortices and confinement
We study the role of percolating clusters of center vortices in configurations of an Ising gauge theory in 3D. It is known that low energy features of gauge theories can be described in terms of an “effective string picture”, and that confinement properties are associated with topologically non-trivial configurations. We focus our attention upon percolating clusters of center vortices, and pres...
متن کامل