The Yang Lee Edge Singularity on Feynman Diagrams

We investigate the Yang-Lee edge singularity on non-planar random graphs, which we consider as the Feynman Diagrams of various d=0 field theories, in order to determine the value of the edge exponent. We consider the hard dimer model on phi3 and phi4 random graphs to test the universality of the exponent with respect to coordination number, and the Ising model in an external field to test its temperature independence. The results here for generic (``thin'') random graphs provide an interesting counterpoint to the discussion by Staudacher of these models on planar random graphs.Comment: LaTeX, 6 pages + 3 figure

Smearing of Coulomb Blockade by Resonant Tunneling

We study the Coulomb blockade in a grain coupled to a lead via a resonant impurity level. We show that the strong energy dependence of the transmission coefficient through the impurity level can have a dramatic effect on the quantization of the grain charge. In particular, if the resonance is sufficiently narrow, the Coulomb staircase shows very sharp steps even if the transmission through the impurity at the Fermi energy is perfect. This is in contrast to the naive expectation that perfect transmission should completely smear charging effects.Comment: 4 pages, 3 figure

A generalised Landau-Lifshitz equation for isotropic SU(3) magnet

In the paper we obtain equations for large-scale fluctuations of the mean field (the field of magnetization and quadrupole moments) in a magnetic system realized by a square (cubic) lattice of atoms with spin s >= 1 at each site. We use the generalized Heisenberg Hamiltonian with biquadratic exchange as a quantum model. A quantum thermodynamical averaging gives classical effective models, which are interpreted as Hamiltonian systems on coadjoint orbits of Lie group SU(3).Comment: 15 pages, 1 figur

Fractional plateaus in the Coulomb blockade of coupled quantum dots

Ground-state properties of a double-large-dot sample connected to a reservoir via a single-mode point contact are investigated. When the interdot transmission is perfect and the dots controlled by the same dimensionless gate voltage, we find that for any finite backscattering from the barrier between the lead and the left dot, the average dot charge exhibits a Coulomb-staircase behavior with steps of size e/2 and the capacitance peak period is halved. The interdot electrostatic coupling here is weak. For strong tunneling between the left dot and the lead, we report a conspicuous intermediate phase in which the fractional plateaus get substantially altered by an increasing slope.Comment: 6 pages, 4 figures, final versio

Topological excitations in 2D spin system with high spin s>=1s>= 1

We construct a class of topological excitations of a mean field in a two-dimensional spin system represented by a quantum Heisenberg model with high powers of exchange interaction. The quantum model is associated with a classical one (the continuous classical analogue) that is based on a Landau-Lifshitz like equation, and describes large-scale fluctuations of the mean field. On the other hand, the classical model is a Hamiltonian system on a coadjoint orbit of the unitary group SU($2s {+} 1$) in the case of spin $s$. We have found a class of mean field configurations that can be interpreted as topological excitations, because they have fixed topological charges. Such excitations change their shapes and grow preserving an energy.Comment: 10 pages, 1 figur

Some New Results on Complex-Temperature Singularities in Potts Models on the Square Lattice

We report some new results on the complex-temperature (CT) singularities of $q$-state Potts models on the square lattice. We concentrate on the problematic region $Re(a) < 0$ (where $a=e^K$) in which CT zeros of the partition function are sensitive to finite lattice artifacts. From analyses of low-temperature series expansions for $3 \le q \le 8$, we establish the existence, in this region, of complex-conjugate CT singularities at which the magnetization and susceptibility diverge. From calculations of zeros of the partition function, we obtain evidence consistent with the inference that these singularities occur at endpoints $a_e, \ a_e^*$ of arcs protruding into the (complex-temperature extension of the) FM phase. Exponents for these singularities are determined; e.g., for $q=3$, we find $\beta_e=-0.125(1)$, consistent with $\beta_e=-1/8$. By duality, these results also imply associated arcs extending to the (CT extension of the) symmetric PM phase. Analytic expressions are suggested for the positions of some of these singularities; e.g., for $q=5$, our finding is consistent with the exact value $a_e,a_e^*=2(-1 \mp i)$. Further discussions of complex-temperature phase diagrams are given.Comment: 26 pages, latex, with eight epsf figure

Controlled Synchronization of One Class of Nonlinear Systems under Information Constraints

Output feedback controlled synchronization problems for a class of nonlinear unstable systems under information constraints imposed by limited capacity of the communication channel are analyzed. A binary time-varying coder-decoder scheme is described and a theoretical analysis for multi-dimensional master-slave systems represented in Lurie form (linear part plus nonlinearity depending only on measurable outputs) is provided. An output feedback control law is proposed based on the Passification Theorem. It is shown that the synchronization error exponentially tends to zero for sufficiantly high transmission rate (channel capacity). The results obtained for synchronization problem can be extended to tracking problems in a straightforward manner, if the reference signal is described by an {external} ({exogenious}) state space model. The results are applied to controlled synchronization of two chaotic Chua systems via a communication channel with limited capacity.Comment: 8 pages, 2 figure

Spin Nematic Phase in S=1 Triangular Antiferromagnets

Spin nematic order is investigated for a S=1 spin model on triangular lattice with bilinear-biquadratic interactions. We particularly studied an antiferro nematic order phase with three-sublattice structure, and magnetic properties are calculated at zero temperature by means of bosonization. Two types of bosonic excitations are found. One is a gapless excitation with linear energy dispersion around $k \sim 0$, and this leads to a finite spin susceptibility at T=0 and would have a specific heat $C(T) \sim T^2$ at low temperatures. These behaviors can explain many of characteristic features of recently discovered spin liquid state in the triangular magnet, NiGa2S4