Unbiased Many-Body calculations with Dyson-Schwinger equations: A novel approach to functional integro-differential equations.

We show how to derive a suitable closed set of functional integro-differential equations based on Dyson-Schwinger equations and introduce the necessary tools to find an unbiased numerical solution. The key concepts are the Homotopy Analysis Method and the adaptation of this semi-analytic method from differential equations to the diagrammatic language of field theory. The resulting diagrams can be summed up by a stochastic sampling procedure. Taking all these techniques into account provides a novel approach to solve the infinite hierarchy of Dyson-Schwinger equations without any truncation.
We illustrate these ideas for the Z₂ symmetric Φ⁴ model in 0 space-time dimensions and show results for the 2-dimensional case which undergoes a second order phase transition belonging to the Ising universality class.