Field theoretic approach to the study of Yang-Lee and Griffiths singularities in the randomly diluted Ising model

Abstract

We study the distribution of zeros of the partition function for the randomly diluted Ising model using field theoretical techniques. Introducing randomness into the pure Ising model causes the distribution of zeros to develop tails in analogy with the density of states in the Anderson localization problem. We show that the density of these Yang-Lee zeros can be calculated using instanton techniques and carry out the calculation for a range of parameters of the model. The nature of Griffiths singularities in this model is controlled by the distribution of the Yang-Lee zeros, and the extensions of the calculation needed for a determination of the actual form of the Griffiths singularities are discussed.