Phase Transitions in the Multicomponent Widom-Rowlinson Model and in Hard Cubes on the BCC--Lattice

We use Monte Carlo techniques and analytical methods to study the phase diagram of the M--component Widom-Rowlinson model on the bcc-lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M greater or equal 3 there is a ``crystal phase'' for z lying between z_c(M) and z_d(M) while for z > z_d(M) there are M demixed phases each consisting mostly of one species. For M=2 there is a direct second order transition from the gas phase to the demixed phase while for M greater or equal 3 the transition at z_d(M) appears to be first order putting it in the Potts model universality class. For M large, Pirogov-Sinai theory gives z_d(M) ~ M-2+2/(3M^2) + ... . In the crystal phase the particles preferentially occupy one of the sublattices, independent of species, i.e. spatial symmetry but not particle symmetry is broken. For M to infinity this transition approaches that of the one component hard cube gas with fugacity y = zM. We find by direct simulations of such a system a transition at y_c ~ 0.71 which is consistent with the simulation z_c(M) for large M. This transition appears to be always of the Ising type.Comment: 11 pages, 4 postscript figures (added in replacement), Physica A (in press

Error-bound formulation for multichannel reception of M-DPSK and pilot-aided M-PSK over Rayleigh-fading channels with postdetection combining

Upper bounds for symbol-error probability are developed for multichannel reception of M-ary phase-shift keying (M-PSK) over frequency-flat Rayleigh-fading channels. Differential coherent demodulation of differentially encoded M-PSK (M-DPSK), pilot-tone aided coherent demodulation of M-PSK (PTA M-CPSK) and pilot-symbol aided coherent demodulation of M-PSK (PSA M-CPSK) are considered in the formulation. The bounds enable the investigation of the effects of fading correlation and unequal average power level between channels using postdetection diversity reception with maximal-ratio combining. Error-performance degradation due to imperfect demodulation effects, such as Doppler spread in M-DPSK schemes, noisy reference signals in PTA M-CPSK, and PSA M-CPSK schemes can be taken into account in the formulation. Exact bit-error probabilities for both binary and quaternary phase-shift keying are also derived.Upper bounds for symbol-error probability are developed for multichannel reception of M-ary phase-shift keying (M-PSK) over frequency-flat Rayleigh-fading channels. Differential coherent demodulation of differentially encoded M-PSK (M-DPSK), pilot-tone aided coherent demodulation of M-PSK (PTA M-CPSK) and pilot-symbol aided coherent demodulation of M-PSK (PSA M-CPSK) are considered in the formulation. The bounds enable the investigation of the effects of fading correlation and unequal average power level between channels using postdetection diversity reception with maximal-ratio combining. Error-performance degradation due to imperfect demodulation effects, such as Doppler spread in M-DPSK schemes, noisy reference signals in PTA M-CPSK, and PSA M-CPSK schemes can be taken into account in the formulation. Exact bit-error probabilities for both binary and quaternary phase-shift keying are also derived

Phase transitions in a system of hard rectangles on the square lattice

The phase diagram of a system of monodispersed hard rectangles of size $m\times m k$ on a square lattice is numerically determined for $m=2,3$ and aspect ratio $k= 1,2,\ldots, 7$. We show the existence of a disordered phase, a nematic phase with orientational order, a columnar phase with orientational and partial translational order, and a solid-like phase with sublattice order, but no orientational order. The asymptotic behavior of the phase boundaries for large $k$ are determined using a combination of entropic arguments and a Bethe approximation. This allows us to generalize the phase diagram to larger $m$ and $k$, showing that for $k \geq 7$, the system undergoes three entropy driven phase transitions with increasing density. The nature of the different phase transitions are established and the critical exponents for the continuous transitions are determined using finite size scaling.Comment: 16 pages, 20 figure

Oblique Confinement and Phase Transitions in Chern-Simons Gauge Theories

We investigate non-perturbative features of a planar Chern-Simons gauge theory modeling the long distance physics of quantum Hall systems, including a finite gap M for excitations. By formulating the model on a lattice, we identify the relevant topological configurations and their interactions. For M bigger than a critical value, the model exhibits an oblique confinement phase, which we identify with Lauglin's incompressible quantum fluid. For M smaller than the critical value, we obtain a phase transition to a Coulomb phase or a confinement phase, depending on the value of the electromagnetic coupling.Comment: 8 pages, harvmac, DFUPG 91/94 and MPI-PhT/94-9

Symbol error rate analysis for M-QAM modulated physical-layer network coding with phase errors

Recent theoretical studies of physical-layer network coding (PNC) show much interest on high-level modulation, such as M-ary quadrature amplitude modulation (M-QAM), and most related works are based on the assumption of phase synchrony. The possible presence of synchronization error and channel estimation error highlight the demand of analyzing the symbol error rate (SER) performance of PNC under different phase errors. Assuming synchronization and a general constellation mapping method, which maps the superposed signal into a set of M coded symbols, in this paper, we analytically derive the SER for M-QAM modulated PNC under different phase errors. We obtain an approximation of SER for general M-QAM modulations, as well as exact SER for quadrature phase-shift keying (QPSK), i.e. 4-QAM. Afterwards, theoretical results are verified by Monte Carlo simulations. The results in this paper can be used as benchmarks for designing practical systems supporting PNC. © 2012 IEEE