4 research outputs found
An Algorithmic Approach to Quantum Field Theory
The lattice formulation provides a way to regularize, define and compute the
Path Integral in a Quantum Field Theory. In this paper we review the
theoretical foundations and the most basic algorithms required to implement a
typical lattice computation, including the Metropolis, the Gibbs sampling, the
Minimal Residual, and the Stabilized Biconjugate inverters. The main emphasis
is on gauge theories with fermions such as QCD. We also provide examples of
typical results from lattice QCD computations for quantities of
phenomenological interest.Comment: 44 pages, to be published in IJMP
Spontaneous magnetization of the Ising model on the Sierpinski carpet fractal, a rigorous result
We give a rigorous proof of the existence of spontaneous magnetization at
finite temperature for the Ising spin model defined on the Sierpinski carpet
fractal. The theorem is inspired by the classical Peierls argument for the two
dimensional lattice. Therefore, this exact result proves the existence of
spontaneous magnetization for the Ising model in low dimensional structures,
i.e. structures with dimension smaller than 2.Comment: 14 pages, 8 figure