A density of states approach to the overlap problem

prob_distMonte-Carlo methods are widely used in theoretical physics, statistical mechanics and condensed matter. Most of the applications have relied on importance sampling, which allows us to evaluate stochastically with a controllable error multi-dimensional integrals of localised functions. In lattice gauge theories, most quantities of interest can be expressed in the path integral formalism as ensemble averages over a positive-definite (and sharply peaked) measure, which provide an ideal scenario for applying importance sampling methods. However, there are noticeable cases in which Monte-Carlo importance sampling methods are either very inefficient or produce inherently wrong results for well understood reasons. Alternatives to importance sampling techniques do exist, but generally they are less efficient in standard cases and hence their use is limited to ad hoc situations in which more standard methods are inapplicable. A very promising method, the LLR algorithm, was recently introduced. The method provides an efficient algorithm to access the density of states of a generic system. Once the density of states is known, the partition function can be reconstructed by performing one-dimensional numerical integrals. In this project we will extend to LLR method to the evaluation of observables that have a poor overlap with the sampled ensemble, with the aim of taking full advantage of the exponential error suppression properties of the LLR method.
Supervisor: Dr Antonio Rago