Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Spin glass phase in the four-state three-dimensional Potts model

We perform numerical simulations, including parallel tempering, a four-state Potts glass model with binary random quenched couplings using the JANUS application-oriented computer. We find and characterize a glassy transition, estimating the critical temperature and the value of the critical exponents. Nevertheless, the extrapolation to infinite volume is hampered by strong scaling corrections. We show that there is no ferromagnetic transition in a large temperature range around the glassy critical temperature. We also compare our results with those obtained recently on the “random permutation” Potts glass.

Near-field diffraction-based focal length determination technique

An accurate and simple technique for determining the focal length of a lens is presented. It consists of measuring the period of the fringes produced by a diffraction grating at the near field when it is illuminated with a beam focused by the unknown lens. In paraxial approximation, the period of the fringes varies linearly with the distance. After some calculations, a simple extrapolation of data is performed to obtain the locations of the principal plane and the focal plane of the lens. Thus, the focal length is obtained as the distance between the two mentioned planes. The accuracy of the method is limited by the collimation degree of the incident beam and by the algorithm used to obtain the period of the fringes. We have checked the technique with two commercial lenses, one convergent and one divergent, with nominal focal lengths (+100±1) mm and (−100±1) mm respectively. We have experimentally obtained the focal lengths resulting into the interval given by the manufacturer but with an uncertainty of 0.1%, one order of magnitude lesser than the uncertainty given by the manufacturer.

Search for VHE gamma-ray emission from Geminga pulsar and nebula with the MAGIC telescopes

The Geminga pulsar, one of the brighest gamma-ray sources, is a promising candidate for emission of very-high-energy (VHE > 100 GeV) pulsed gamma rays. Also, detection of a large nebula have been claimed by water Cherenkov instruments. We performed deep observations of Geminga with the MAGIC telescopes, yielding 63 hours of good-quality data, and searched for emission from the pulsar and pulsar wind nebula. We did not find any significant detection, and derived 95% confidence level upper limits. The resulting upper limits of 5.3 × 10^(−13) TeV cm^(−2)s^(−1) for the Geminga pulsar and 3.5 × 10^(−12) TeV cm^(−2)s^(−1) for the surrounding nebula at 50 GeV are the most constraining ones obtained so far at VHE. To complement the VHE observations, we also analyzed 5 years of Fermi-LAT data from Geminga, finding that the sub-exponential cut-off is preferred over the exponential cut-off that has been typically used in the literature. We also find that, above 10 GeV, the gamma-ray spectra from Geminga can be described with a power law with index softer than 5. The extrapolation of the power-law Fermi-LAT pulsed spectra to VHE goes well below the MAGIC upper limits, indicating that the detection of pulsed emission from Geminga with the current generation of Cherenkov telescopes is very difficult.

Hybrid Monte Carlo algorithm for the double exchange model

The Hybrid Monte Carlo algorithm is adapted to the simulation of a system of classical degrees of freedom coupled to non self-interacting lattices fermions. The diagonalization of the Hamiltonian matrix is avoided by introducing a path-integral formulation of the problem, in d + 1 Euclidean space–time. A perfect action formulation allows to work on the continuum Euclidean time, without need for a Trotter–Suzuki extrapolation. To demonstrate the feasibility of the method we study the Double Exchange Model in three dimensions. The complexity of the algorithm grows only as the system volume, allowing to simulate in lattices as large as 163 on a personal computer. We conclude that the second order paramagnetic–ferromagnetic phase transition of Double Exchange Materials close to half-filling belongs to the Universality Class of the three-dimensional classical Heisenberg model.

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.