Monte Carlo computation of the spectral density function in the interacting scalar field theory

We study the [Formula: see text] field theory in d = 4. Using bold diagrammatic Monte Carlo method, we solve the Schwinger–Dyson equations and find the spectral density function of the theory beyond the weak coupling regime. We then compare our result with the one obtained from the perturbation theory. At the end, we utilize our Monte Carlo result to find the vertex function as the basis for the computation of the physical scattering amplitudes.

TENSOR RENORMALIZATION GROUP APPROACH TO A LATTICE BOSON MODEL

A method to apply the tensor renormalization group to a lattice boson model is proposed. It is based on the truncated singular value decomposition of a compact operator. We demonstrate it using the (1+1)-dimensional ϕ4 model. The evaluated critical points on the lattice are consistent with the Monte Carlo result.

Five-Loop Critical Temperature Shift in Weakly Interacting Homogeneous Bose–Einstein Condensate

Using variational perturbation theory, we calculate the shift in the critical temperature Tcup to five loops to lowest order in the scattering length a and find [Formula: see text], where n is the particle density. Our result is slightly lower than the latest Monte Carlo result (1.32±0.02) an1/3.

A theoretical simulation of bulk water

A new formulation developed at this laboratory has been used in the study of a water cluster with 65 molecules. The fact that the calculated average potential energy per molecule agrees with the Monte Carlo result at 300 K suggests that this method, which is fast and inexpensive, might be used to obtain estimates of such energies for other systems as well as in generating starting configurations for Monte Carlo calculations.