Entropy of chains placed on the square lattice

We obtain the entropy of flexible linear chains composed of M monomers placed on the square lattice using a transfer matrix approach. An excluded volume interaction is included by considering the chains to be self-and mutually avoiding, and a fraction rho of the sites are occupied by monomers. We solve the problem exactly on stripes of increasing width m and then extrapolate our results to the two-dimensional limit to infinity using finite-size scaling. The extrapolated results for several finite values of M and in the polymer limit M to infinity for the cases where all lattice sites are occupied (rho=1) and for the partially filled case rho<1 are compared with earlier results. These results are exact for dimers (M=2) and full occupation (\rho=1) and derived from series expansions, mean-field like approximations, and transfer matrix calculations for some other cases. For small values of M, as well as for the polymer limit M to infinity, rather precise estimates of the entropy are obtained.Comment: 6 pages, 7 figure

The use of synchrotron edge topography to study polytype nearest neighbour relationships in SiC

A brief review of the phenomenon of polytypism is presented and its prolific abundance in Silicon Carbide discussed. An attempt has been made to emphasise modern developments in understanding this unique behaviour. The properties of Synchrotron Radiation are shown to be ideally suited to studies of polytypes in various materials and in particular the coalescence of polytypes in SiC. It is shown that with complex multipolytypic crystals the technique of edge topography allows the spatial extent of disorder to be determined and, from the superposition of Laue type reflections, neighbourhood relationships between polytypes can be deduced. Finer features have now been observed with the advent of second generation synchrotrons, the resolution available enabling the regions between adjoining polytypes to be examined more closely. It is shown that Long Period Polytypes and One Dimensionally Disordered layers often found in association with regions of high defect density are common features at polytype boundaries. An idealised configuration termed a "polytype sandwich" is presented as a model for the structure of SiC grown by the modified Lely technique. The frequency of common sandwich edge profiles are classified and some general trends of polytype neighbourism are summarised

Pocket Monte Carlo algorithm for classical doped dimer models

We study the correlations of classical hardcore dimer models doped with monomers by Monte Carlo simulation. We introduce an efficient cluster algorithm, which is applicable in any dimension, for different lattices and arbitrary doping. We use this algorithm for the dimer model on the square lattice, where a finite density of monomers destroys the critical confinement of the two-monomer problem. The monomers form a two-component plasma located in its high-temperature phase, with the Coulomb interaction screened at finite densities. On the triangular lattice, a single pair of monomers is not confined. The monomer correlations are extremely short-ranged and hardly change with doping.Comment: 6 pages, REVTeX

Neutrino Observatories Can Characterize Cosmic Sources and Neutrino Properties

Neutrino telescopes that measure relative fluxes of ultrahigh-energy $\nu_{e}, \nu_{\mu}, \nu_{\tau}$ can give information about the location and characteristics of sources, about neutrino mixing, and can test for neutrino instability and for departures from CPT invariance in the neutrino sector. We investigate consequences of neutrino mixing for the neutrino flux arriving at Earth, and consider how terrestrial measurements can characterize distant sources. We contrast mixtures that arise from neutrino oscillations with those signaling neutrino decays. We stress the importance of measuring $\nu_{e}, \nu_{\mu}, \nu_{\tau}$ fluxes in neutrino observatories.Comment: 9 RevTeX pages, 4 figure

Exact multilocal renormalization on the effective action : application to the random sine Gordon model statics and non-equilibrium dynamics

We extend the exact multilocal renormalization group (RG) method to study the flow of the effective action functional. This important physical quantity satisfies an exact RG equation which is then expanded in multilocal components. Integrating the nonlocal parts yields a closed exact RG equation for the local part, to a given order in the local part. The method is illustrated on the O(N) model by straightforwardly recovering the $\eta$ exponent and scaling functions. Then it is applied to study the glass phase of the Cardy-Ostlund, random phase sine Gordon model near the glass transition temperature. The static correlations and equilibrium dynamical exponent $z$ are recovered and several new results are obtained. The equilibrium two-point scaling functions are obtained. The nonequilibrium, finite momentum, two-time $t,t'$ response and correlations are computed. They are shown to exhibit scaling forms, characterized by novel exponents $\lambda_R \neq \lambda_C$, as well as universal scaling functions that we compute. The fluctuation dissipation ratio is found to be non trivial and of the form $X(q^z (t-t'), t/t')$. Analogies and differences with pure critical models are discussed.Comment: 33 pages, RevTe

Random walks and polymers in the presence of quenched disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models', where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points : thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble of samples $(i)$ of size $L$. We describe the results of this analysis for the bidimensional wetting and for the Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S., France, November 200

Determining the thermal histories of Apollo 15 mare basalts using diffusion modelling in olivine

Mare basalts collected at the Apollo 15 landing site can be classified into two groups. Based on differing whole-rock major element chemistry, these groups are the quartz-normative basalt suite and the olivine-normative basalt suite. In this study we use modelling of Fe-Mg interdiffusion in zoned olivine crystals to investigate the magmatic environments in which the zonation was formed, be that within the lunar crust or during cooling within a surficial lava flow, helping to understand the thermal histories of the two basalt suites. Interdiffusion of Fe-Mg in olivine was modelled in 29 crystals in total, from six olivine-normative basalt thin sections and from three quartz-normative basalt thin sections. We used a dynamic diffusion model that includes terms for both crystal growth and intracrystalline diffusion during magma cooling. Calculated diffusion timescales range from 5 to 24 days for quartz-normative samples, and 6 to 91 days for olivine-normative samples. Similarities in diffusion timescales point to both suites experiencing similar thermal histories and eruptive processes. The diffusion timescales are short (between 5 and 91 days), and compositional zonation is dominated by crystal growth, which indicates that the diffusion most likely took place during cooling and solidification within lava flows at the lunar surface. We used a simple conductive cooling model to link our calculated diffusion timescales with possible lava flow thicknesses, and from this we estimate that Apollo 15 lava flows are a minimum of 3–6 m thick. This calculation is consistent with flow thickness estimates from photographs of lava flows exposed in the walls of Hadley Rille at the Apollo 15 landing site. Our study demonstrates that diffusion modelling is a valuable method of obtaining information about lunar magmatic environments recorded by individual crystals within mare basalt samples

Exact renormalization group flow equations for non-relativistic fermions: scaling towards the Fermi surface

We construct exact functional renormalization group (RG) flow equations for non-relativistic fermions in arbitrary dimensions, taking into account not only mode elimination but also the rescaling of the momenta, frequencies and the fermionic fields. The complete RG flow of all relevant, marginal and irrelevant couplings can be described by a system of coupled flow equations for the irreducible n-point vertices. Introducing suitable dimensionless variables, we obtain flow equations for generalized scaling functions which are continuous functions of the flow parameter, even if we consider quantities which are dominated by momenta close to the Fermi surface, such as the density-density correlation function at long wavelengths. We also show how the problem of constructing the renormalized Fermi surface can be reduced to the problem of finding the RG fixed point of the irreducible two-point vertex at vanishing momentum and frequency. We argue that only if the degrees of freedom are properly rescaled it is possible to reach scale-invariant non-Fermi liquid fixed points within a truncation of the exact RG flow equations.Comment: 20 Revtex pages, with 4 figures; final version to appear in Phys. Rev. B; references and some explanations adde

Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices

We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three, four or five, where one of the outmost vertices is not covered when the number of vertices $v(n)$ is an odd number. The entropy of absorption of diatomic molecules per site, defined as $S_{SG_d}=\lim_{n \to \infty} \ln N_d(n)/v(n)$, is calculated to be $\ln(2)/3$ exactly for $SG_2(n)$. The numbers of dimers on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4,5$ are also obtained exactly. Their entropies are equal to $\ln(6)/7$, $\ln(28)/12$, $\ln(200)/18$, respectively. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for $SG_d(n)$ with $d=3,4,5$. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of $S_{SG_d}$ with $d=3,4,5$ can be evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl

Apparent phase transitions in finite one-dimensional sine-Gordon lattices

We study the one-dimensional sine-Gordon model as a prototype of roughening phenomena. In spite of the fact that it has been recently proven that this model can not have any phase transition [J. A. Cuesta and A. Sanchez, J. Phys. A 35, 2373 (2002)], Langevin as well as Monte Carlo simulations strongly suggest the existence of a finite temperature separating a flat from a rough phase. We explain this result by means of the transfer operator formalism and show as a consequence that sine-Gordon lattices of any practically achievable size will exhibit this apparent phase transition at unexpectedly large temperatures.Comment: 7 pages, 4 figure