Distribution of partition function zeros of the ±J\pm J model on the Bethe lattice

The distribution of partition function zeros is studied for the $\pm J$ model of spin glasses on the Bethe lattice. We find a relation between the distribution of complex cavity fields and the density of zeros, which enables us to obtain the density of zeros for the infinite system size by using the cavity method. The phase boundaries thus derived from the location of the zeros are consistent with the results of direct analytical calculations. This is the first example in which the spin glass transition is related to the distribution of zeros directly in the thermodynamical limit. We clarify how the spin glass transition is characterized by the zeros of the partition function. It is also shown that in the spin glass phase a continuous distribution of singularities touches the axes of real field and temperature.Comment: 23 pages, 12 figure

Statistical mechanical analysis of a hierarchical random code ensemble in signal processing

We study a random code ensemble with a hierarchical structure, which is closely related to the generalized random energy model with discrete energy values. Based on this correspondence, we analyze the hierarchical random code ensemble by using the replica method in two situations: lossy data compression and channel coding. For both the situations, the exponents of large deviation analysis characterizing the performance of the ensemble, the distortion rate of lossy data compression and the error exponent of channel coding in Gallager's formalism, are accessible by a generating function of the generalized random energy model. We discuss that the transitions of those exponents observed in the preceding work can be interpreted as phase transitions with respect to the replica number. We also show that the replica symmetry breaking plays an essential role in these transitions.Comment: 24 pages, 4 figure

Replica analysis of partition-function zeros in spin-glass models

We study the partition-function zeros in mean-field spin-glass models. We show that the replica method is useful to find the locations of zeros in a complex parameter plane. For the random energy model, we obtain the phase diagram in the plane and find that there are two types of distribution of zeros: two-dimensional distribution within a phase and one-dimensional one on a phase boundary. Phases with a two-dimensional distribution are characterized by a novel order parameter defined in the present replica analysis. We also discuss possible patterns of distributions by studying several systems.Comment: 23 pages, 12 figures; minor change

On analyticity with respect to the replica number in random energy models I: an exact expression of the moment of the partition function

We provide an exact expression of the moment of the partition function for random energy models of finite system size, generalizing an earlier expression for a grand canonical version of the discrete random energy model presented by the authors in Prog. Theor. Phys. 111, 661 (2004). The expression can be handled both analytically and numerically, which is useful for examining how the analyticity of the moment with respect to the replica numbers, which play the role of powers of the moment, can be broken in the thermodynamic limit. A comparison with a replica method analysis indicates that the analyticity breaking can be regarded as the origin of the one-step replica symmetry breaking. The validity of the expression is also confirmed by numerical methods for finite systems.Comment: 16 pages, 4 figure

The Infrared Imaging Spectrograph (IRIS) for TMT: Instrument Overview

We present an overview of the design of IRIS, an infrared (0.84 - 2.4 micron) integral field spectrograph and imaging camera for the Thirty Meter Telescope (TMT). With extremely low wavefront error (<30 nm) and on-board wavefront sensors, IRIS will take advantage of the high angular resolution of the narrow field infrared adaptive optics system (NFIRAOS) to dissect the sky at the diffraction limit of the 30-meter aperture. With a primary spectral resolution of 4000 and spatial sampling starting at 4 milliarcseconds, the instrument will create an unparalleled ability to explore high redshift galaxies, the Galactic center, star forming regions and virtually any astrophysical object. This paper summarizes the entire design and basic capabilities. Among the design innovations is the combination of lenslet and slicer integral field units, new 4Kx4k detectors, extremely precise atmospheric dispersion correction, infrared wavefront sensors, and a very large vacuum cryogenic system.Comment: Proceedings of the SPIE, 9147-76 (2014

The Infrared Imaging Spectrograph (IRIS) for TMT: Optical design of IRIS imager with "co-axis double TMA"

IRIS (InfraRed Imaging Spectrograph) is one of the first-generation instruments for the Thirty Meter Telescope (TMT). IRIS is composed of a combination of near-infrared (0.84-2.4 μm) diffraction limited imager and integral field spectrograph. To achieve near-diffraction limited resolutions in the near-infrared wavelength region, IRIS uses the advanced adaptive optics system NFIRAOS (Narrow Field Infrared Adaptive Optics System) and integrated on-instrument wavefront sensors (OIWFS). However, IRIS itself has challenging specifications. First, the overall system wavefront error should be less than 40 nm in Y, z, J, and H-band and 42 nm in K-band over a 34.0 × 34.0 arcsecond field of view. Second, the throughput of the imager components should be more than 42 percent. To achieve the extremely low wavefront error and high throughput, all reflective design has been newly proposed. We have adopted a new design policy called "Co-Axis double-TMA", which cancels the asymmetric aberrations generated by "collimator/TMA" and "camera/TMA" efficiently. The latest imager design meets all specifications, and, in particular, the wavefront error is less than 17.3 nm and throughput is more than 50.8 percent. However, to meet the specification of wavefront error and throughput as built performance, the IRIS imager requires both mirrors with low surface irregularity after high-reflection coating in cryogenic and high-level Assembly Integration and Verification (AIV). To deal with these technical challenges, we have done the tolerance analysis and found that total pass rate is almost 99 percent in the case of gauss distribution and more than 90 percent in the case of parabolic distribution using four compensators. We also have made an AIV plan and feasibility check of the optical elements. In this paper, we will present the details of this optical syste

The infrared imaging spectrograph (IRIS) for TMT: status report for IRIS imager

The current status of IRIS imager at NAOJ is reported. IRIS (Infrared Imaging Spectrograph) is a first light instrument of TMT (Thirty Meter Telescope). IRIS has just passed the preliminary design review and moved forward to the final design phase. In this paper, optical and mechanical design of IRIS imager and prototyping activities conducted during the preliminary design phase are summarized

Belief Propagation for Error Correcting Codes and Lossy Compression Using Multilayer Perceptrons

The belief propagation (BP) based algorithm is investigated as a potential decoder for both of error correcting codes and lossy compression, which are based on non-monotonic tree-like multilayer perceptron encoders. We discuss that whether the BP can give practical algorithms or not in these schemes. The BP implementations in those kind of fully connected networks unfortunately shows strong limitation, while the theoretical results seems a bit promising. Instead, it reveals it might have a rich and complex structure of the solution space via the BP-based algorithms.Comment: 18 pages, 18 figure