Hamiltonian Analysis of Gauged CP1CP^1 Model, the Hopf term, and fractional spin

Recently it was shown by Cho and Kimm that the gauged $CP^1$ model, obtained by gauging the global $SU(2)$ group and adding a corresponding Chern-Simons term, has got its own soliton. These solitons are somewhat distinct from those of pure $CP^1$ model as they cannot always be characterised by $\pi_2(CP^1)=Z$. In this paper, we first carry out a detailed Hamiltonian analysis of this gauged $CP^1$ model. This reveals that the model has only $SU(2)$ as the gauge invariance, rather than $SU(2) \times U(1)$. The $U(1)$ gauge invariance of the original (ungauged) $CP^1$ model is actually contained in the $SU(2)$ group itself. Then we couple the Hopf term associated to these solitons and again carry out its Hamiltonian analysis. The symplectic structures, along with the structures of the constraints of these two models (with or without Hopf term) are found to be essentially the same. The model with a Hopf term is shown to have fractional spin which, when computed in the radiation gauge, is found to depend not only on the soliton number $N$, but also on the nonabelian charge. We then carry out a reduced (partially) phase space analysis in a different physical sector of the model where the degrees of freedom associated with the $CP^1$ fields are transformed away. The model now reduces to a $U(1)$ gauge theory with two Chern-Simons gauge fields getting mass-like terms and one remaining massless. In this case the fractional spin is computed in terms of the dynamical degrees of freedom and shown to depend purely on the charge of the surviving abelian symmetry. Although this reduced model is shown to have its own solitonic configuration, it turns out to be trivial.Comment: Latex, 26 pages, accepted for publication in Phys. Rev.

Statistics of Multiple Sign Changes in a Discrete Non-Markovian Sequence

We study analytically the statistics of multiple sign changes in a discrete non-Markovian sequence ,\psi_i=\phi_i+\phi_{i-1} (i=1,2....,n) where \phi_i's are independent and identically distributed random variables each drawn from a symmetric and continuous distribution \rho(\phi). We show that the probability P_m(n) of m sign changes upto n steps is universal, i.e., independent of the distribution \rho(\phi). The mean and variance of the number of sign changes are computed exactly for all n>0. We show that the generating function {\tilde P}(p,n)=\sum_{m=0}^{\infty}P_m(n)p^m\sim \exp[-\theta_d(p)n] for large n where the `discrete' partial survival exponent \theta_d(p) is given by a nontrivial formula, \theta_d(p)=\log[{{\sin}^{-1}(\sqrt{1-p^2})}/{\sqrt{1-p^2}}] for 0\le p\le 1. We also show that in the natural scaling limit when m is large, n is large but but keeping x=m/n fixed, P_m(n)\sim \exp[-n \Phi(x)] where the large deviation function \Phi(x) is computed. The implications of these results for Ising spin glasses are discussed.Comment: 4 pages revtex, 1 eps figur

Zero Temperature Dynamics of the Weakly Disordered Ising Model

The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising model is studied at zero-temperature. A single characteristic length scale, $L(t)$, is extracted from the equal time correlation function. In the pure case, the persistence probability decreases algebraically with the coarsening length scale. In the disordered case, three distinct regimes are identified: a short time regime where the behaviour is pure-like; an intermediate regime where the persistence probability decays non-algebraically with time; and a long time regime where the domains freeze and there is a cessation of growth. In the intermediate regime, we find that $P(t)\sim L(t)^{-\theta'}$, where $\theta' = 0.420\pm 0.009$. The value of $\theta'$ is consistent with that found for the pure 2d Ising model at zero-temperature. Our results in the intermediate regime are consistent with a logarithmic decay of the persistence probability with time, $P(t)\sim (\ln t)^{-\theta_d}$, where $\theta_d = 0.63\pm 0.01$.Comment: references updated, very minor amendment to abstract and the labelling of figures. To be published in Phys Rev E (Rapid Communications), 1 March 199

Global Persistence Exponent for Critical Dynamics

A `persistence exponent' $\theta$ is defined for nonequilibrium critical phenomena. It describes the probability, $p(t) \sim t^{-\theta}$, that the global order parameter has not changed sign in the time interval $t$ following a quench to the critical point from a disordered state. This exponent is calculated in mean-field theory, in the $n=\infty$ limit of the $O(n)$ model, to first order in $\epsilon = 4-d$, and for the 1-d Ising model. Numerical results are obtained for the 2-d Ising model. We argue that $\theta$ is a new independent exponent.Comment: 4 pages, revtex, one figur

Magnetic phase diagram of spatially anisotropic, frustrated spin-1/2 Heisenberg antiferromagnet on a stacked square lattice

Magnetic phase diagram of a spatially anisotropic, frustrated spin-1/2 Heisenberg antiferromagnet on a stacked square lattice is investigated using second-order spin-wave expansion. The effects of interlayer coupling and the spatial anisotropy on the magnetic ordering of two ordered ground states are explicitly studied. It is shown that with increase in next nearest neighbor frustration the second-order corrections play a significant role in stabilizing the magnetization. We obtain two ordered magnetic phases (Neel and stripe) separated by a paramagnetic disordered phase. Within second-order spin-wave expansion we find that the width of the disordered phase diminishes with increase in the interlayer coupling or with decrease in spatial anisotropy but it does not disappear. Our obtained phase diagram differs significantly from the phase diagram obtained using linear spin-wave theory.Comment: 22 pages, 6 figures, minor changes from previous versio

Evolution of primordial black holes in Jordan-Brans-Dicke cosmology

We consider the evolution of primordial black holes in a generalyzed Jordan-Brans-Dicke cosmological model where both the Brans-Dicke scalar field and its coupling to gravity are dynamical functions determined from the evolution equations. The evaporation rate for the black holes changes compared to that in standard cosmology. We show that accretion of radiation can proceed effectively in the radiation dominated era. The black hole lifetime shortens for low initial mass, but increases for high initial mass, and is thus considerably modified compared to the case of standard cosmology. We derive a cut-off value for the initial black hole mass, below which primordial black holes evaporate out in the radiation dominated era, and above which they survive beyond the present era.Comment: 5 pages, Latex; uses MNRAS stylefiles; minor changes; accepted for publication in MNRA

Exact Occupation Time Distribution in a Non-Markovian Sequence and Its Relation to Spin Glass Models

We compute exactly the distribution of the occupation time in a discrete {\em non-Markovian} toy sequence which appears in various physical contexts such as the diffusion processes and Ising spin glass chains. The non-Markovian property makes the results nontrivial even for this toy sequence. The distribution is shown to have non-Gaussian tails characterized by a nontrivial large deviation function which is computed explicitly. An exact mapping of this sequence to an Ising spin glass chain via a gauge transformation raises an interesting new question for a generic finite sized spin glass model: at a given temperature, what is the distribution (over disorder) of the thermally averaged number of spins that are aligned to their local fields? We show that this distribution remains nontrivial even at infinite temperature and can be computed explicitly in few cases such as in the Sherrington-Kirkpatrick model with Gaussian disorder.Comment: 10 pages Revtex (two-column), 1 eps figure (included

Little evidence for entropy and energy excess beyond r500r_{500} - An end to ICM preheating?

Non-gravitational feedback affects the nature of the intra-cluster medium (ICM). X-ray cooling of the ICM and in situ energy feedback from AGN's and SNe as well as {\it preheating} of the gas at epochs preceding the formation of clusters are proposed mechanisms for such feedback. While cooling and AGN feedbacks are dominant in cluster cores, the signatures of a preheated ICM are expected to be present even at large radii. To estimate the degree of preheating, with minimum confusion from AGN feedback/cooling, we study the excess entropy and non-gravitational energy profiles upto $r_{200}$ for a sample of 17 galaxy clusters using joint data sets of {\it Planck} SZ pressure and {\it ROSAT/PSPC} gas density profiles. The canonical value of preheating entropy floor of $\gtrsim 300$ keV cm$^2$, needed in order to match cluster scalings, is ruled out at $\approx 3\sigma$. We also show that the feedback energy of 1 keV/particle is ruled out at 5.2$\sigma$ beyond $r_{500}$. Our analysis takes both non-thermal pressure and clumping into account which can be important in outer regions. Our results based on the direct probe of the ICM in the outermost regions do not support any significant preheating.Comment: 6 pages, 4 figures, 1 table, Accepted in MNRAS Letter