Fisher's zeros of quasi-Gaussian densities of states

We discuss apparent paradoxes regarding the location of the zeros of the partition function in the complex $\beta$ plane (Fisher's zeros) of a pure SU(2) lattice gauge theory in 4 dimensions. We propose a new criterion to draw the region of the complex $\beta$ plane where reweighting methods can be trusted when the density of states is almost but not exactly Gaussian. We propose new methods to infer the existence of zeros outside of this region. We demonstrate the reliability of these proposals with quasi Gaussian Monte Carlo distributions where the locations of the zeros can be calculated by independent numerical methods. The results are presented in such way that the methods can be applied for general lattice models. Applications to specific lattice models will be discussed in a separate publication.Comment: 11 pages, 21 figures, with minor correction

Density of states and Fisher's zeros in compact U(1) pure gauge theory

We present high-accuracy calculations of the density of states using multicanonical methods for lattice gauge theory with a compact gauge group U(1) on 4^4, 6^4 and 8^4 lattices. We show that the results are consistent with weak and strong coupling expansions. We present methods based on Chebyshev interpolations and Cauchy theorem to find the (Fisher's) zeros of the partition function in the complex beta=1/g^2 plane. The results are consistent with reweighting methods whenever the latter are accurate. We discuss the volume dependence of the imaginary part of the Fisher's zeros, the width and depth of the plaquette distribution at the value of beta where the two peaks have equal height. We discuss strategies to discriminate between first and second order transitions and explore them with data at larger volume but lower statistics. Higher statistics and even larger lattices are necessary to draw strong conclusions regarding the order of the transition.Comment: 14 pages, 16 figure

Development of a site-specific standard for selenium in open waters of Great Salt Lake, Utah

Great Salt Lake is a unique terminal lake located adjacent to Salt Lake City, Utah. Beneficial uses of Great Salt Lake are protected through application of a narrative clause in the state water quality standards. The Utah Division of Water Quality initiated a process in 2004 to develop a site-specific water quality standard for selenium for open waters of Great Salt Lake in response to specific concerns expressed by the public. The process the Division of Water Quality initiated included formation of a stakeholders\u27 Steering Committee and a Science Panel to identify the required studies, manage those studies, and recommend a site specific standard. Studies were recently completed to assess concentrations and effects of selenium in five species of birds; measure selenium concentrations of water, seston, brine shrimp (Artemia sp.), and brine flies (Ephydra sp.); measure selenium loads entering Great Salt Lake; and measure flux of selenium from water to sediment, atmosphere and the food web. Information from these studies was used to populate the elements of a comprehensive conceptual model for Great Salt Lake that is being used to establish the site-specific standard for selenium

Fisher's zeros as boundary of renormalization group flows in complex coupling spaces

We propose new methods to extend the renormalization group transformation to complex coupling spaces. We argue that the Fisher's zeros are located at the boundary of the complex basin of attraction of infra-red fixed points. We support this picture with numerical calculations at finite volume for two-dimensional O(N) models in the large-N limit and the hierarchical Ising model. We present numerical evidence that, as the volume increases, the Fisher's zeros of 4-dimensional pure gauge SU(2) lattice gauge theory with a Wilson action, stabilize at a distance larger than 0.15 from the real axis in the complex beta=4/g^2 plane. We discuss the implications for proofs of confinement and searches for nontrivial infra-red fixed points in models beyond the standard model.Comment: 4 pages, 3 fig