Perturbative Ward identities for Yang-Mills field theory stochastically quantized

%'e compute the divergent part of the three-point vertex function of the non-Abelian Yang-Mills gauge field theory within the stochastic quantization approach to the one-loop order. This calculation allows us to find four renormalization constants which, together with the four previously obtained, verify, to the calculated order, some Ward identities.

Improved and customized secondary optics for photo-voltaic concentrators

In this contribution the line flow method is applied to an optimized secondary optics in a photovoltaic concentration system where the primary optics is already defined and characterized. This method is a particular application of photic field theory. This method uses the parameterization of a given primary optics, including actual tolerances of the manufacturing process. The design of the secondary optics is constrained by the selection of primary optics and maximizes the concentration at a previously specified collection area. The geometry of the secondary element is calculated by using a virtual source, which sends light in a first concentration step. This allows us to calculate the line flow for this specific case. This concept allows designing more compact and efficient secondary optics of photovoltaic systems.

Mean-value identities as an opportunity for Monte Carlo error reduction

In the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control variates to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the twodimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.

Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1|1) permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low-energy excitations and the low-temperature behavior of the free energy, which coincides with that of a (1+1)-dimensional conformal field theory (CFT) with central charge c=1 when the chemical potential lies in the critical interval (0,E(π)), E(p) being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson (1+1)-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge c=1. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su(1|1) elliptic chain.

On the universality class of monopole percolation in scalar QED

We study the critical properties of the monopole-percolation transition in U(1) lattice gauge theory coupled to scalars at infinite (β = 0) gauge coupling. We find strong scaling corrections in the critical exponents that must be considered by means of an infinite-volume extrapolation. After the extrapolation, our results are as precise as the obtained for the four dimensional site-percolation and, contrary to previously stated, fully compatible with them.