Phase transitions in self-dual generalizations of the Baxter-Wu model

We study two types of generalized Baxter-Wu models, by means of transfer-matrix and Monte Carlo techniques. The first generalization allows for different couplings in the up- and down triangles, and the second generalization is to a $q$-state spin model with three-spin interactions. Both generalizations lead to self-dual models, so that the probable locations of the phase transitions follow. Our numerical analysis confirms that phase transitions occur at the self-dual points. For both generalizations of the Baxter-Wu model, the phase transitions appear to be discontinuous.Comment: 29 pages, 13 figure

Exact Solution of an Octagonal Random Tiling Model

We consider the two-dimensional random tiling model introduced by Cockayne, i.e. the ensemble of all possible coverings of the plane without gaps or overlaps with squares and various hexagons. At the appropriate relative densities the correlations have eight-fold rotational symmetry. We reformulate the model in terms of a random tiling ensemble with identical rectangles and isosceles triangles. The partition function of this model can be calculated by diagonalizing a transfer matrix using the Bethe Ansatz (BA). The BA equations can be solved providing {\em exact} values of the entropy and elastic constants.Comment: 4 pages,3 Postscript figures, uses revte

Bethe Ansatz solution of a decagonal rectangle triangle random tiling

A random tiling of rectangles and triangles displaying a decagonal phase is solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square triangle and the octagonal rectangle triangle tiling an exact expression for the maximum of the entropy is found.Comment: 17 pages, 4 figures, some remarks added and typos correcte

Phase transition and critical properties of spin-orbital interacting systems

Phase transition and critical properties of Ising-like spin-orbital interacting systems in 2-dimensional triangular lattice are investigated. We first show that the ground state of the system is a composite spin-orbital ferro-ordered phase. Though Landau effective field theory predicts the second-order phase transition of the composite spin-orbital order, however, the critical exponents obtained by the renormalization group approach demonstrate that the spin-orbital order-disorder transition is far from the second-order, rather, it is more close to the first-order, implying that the widely observed first-order transition in many transition-metal oxides may be intrinsic. The unusual critical behavior near the transition point is attributed to the fractionalization of the composite order parameter.Comment: Accepted to Phys. Lett.

A Cluster Method for the Ashkin--Teller Model

A cluster Monte Carlo algorithm for the Ashkin-Teller (AT) model is constructed according to the guidelines of a general scheme for such algorithms. Its dynamical behaviour is tested for the square lattice AT model. We perform simulations on the line of critical points along which the exponents vary continuously, and find that critical slowing down is significantly reduced. We find continuous variation of the dynamical exponent $z$ along the line, following the variation of the ratio $\alpha/\nu$, in a manner which satisfies the Li-Sokal bound $z_{cluster}\geq\alpha/\nu$, that was so far proved only for Potts models.Comment: 18 pages, Revtex, figures include

Network Harness: Metropolis Public Transport

We analyze the public transport networks (PTNs) of a number of major cities of the world. While the primary network topology is defined by a set of routes each servicing an ordered series of given stations, a number of different neighborhood relations may be defined both for the routes and the stations. The networks defined in this way display distinguishing properties, the most striking being that often several routes proceed in parallel for a sequence of stations. Other networks with real-world links like cables or neurons embedded in two or three dimensions often show the same feature - we use the car engineering term "harness" for such networks. Geographical data for the routes reveal surprising self-avoiding walk (SAW) properties. We propose and simulate an evolutionary model of PTNs based on effectively interacting SAWs that reproduces the key features.Comment: 5 pages, 4 figure

Dynamics near the Surface Reconstruction of W(100)

Using Brownian molecular dynamics simulation, we study the surface dynamics near the reconstruction transition of W(100) via a model Hamiltonian. Results for the softening and broadening of the surface phonon spectrum near the transition are compared with previous calculations and with He atom scattering data. From the critical behavior of the central peak in the dynamical structure factor, we also estimate the exponent of the power law anomaly for adatom diffusion near the transition temperature.Comment: 8 pages, 8 figures, to appear in Phys. Rev.

Charge 4e4e superconductivity from pair density wave order in certain high temperature superconductors

A number of spectacular experimental anomalies\cite{li-2007,fujita-2005} have recently been discovered in certain cuprates, notably {\LBCO} and {\LNSCO}, which exhibit unidirectional spin and charge order (known as ``stripe order''). We have recently proposed to interpret these observations as evidence for a novel ``striped superconducting'' state, in which the superconducting order parameter is modulated in space, such that its average is precisely zero. Here, we show that thermal melting of the striped superconducting state can lead to a number of unusual phases, of which the most novel is a charge $4e$ superconducting state, with a corresponding fractional flux quantum $hc/4e$. These are never-before observed states of matter, and ones, moreover, that cannot arise from the conventional Bardeen-Cooper-Schrieffer (BCS) mechanism. Thus, direct confirmation of their existence, even in a small subset of the cuprates, could have much broader implications for our understanding of high temperature superconductivity. We propose experiments to observe fractional flux quantization, which thereby could confirm the existence of these states.Comment: 5 pages, 2 figures; new version in Nature Physics format with a discussion of the effective Josephson coupling J2 and minor changes. Mildly edited abstract. v3: corrected versio

Peculiar scaling of self-avoiding walk contacts

The nearest neighbor contacts between the two halves of an N-site lattice self-avoiding walk offer an unusual example of scaling random geometry: for N going to infinity they are strictly finite in number but their radius of gyration Rc is power law distributed, ~ Rc^{-\tau}, where \tau>1 is a novel exponent characterizing universal behavior. A continuum of diverging lengths scales is associated to the Rc distribution. A possibly super-universal \tau=2 is also expected for the contacts of a self-avoiding or random walk with a confining wall.Comment: 4 pages, 5 Postscript figures, uses psfig.sty; some sentences clarifie

Dynamic critical behavior of the Swendsen--Wang Algorithm for the three-dimensional Ising model

We have performed a high-precision Monte Carlo study of the dynamic critical behavior of the Swendsen-Wang algorithm for the three-dimensional Ising model at the critical point. For the dynamic critical exponents associated to the integrated autocorrelation times of the "energy-like" observables, we find z_{int,N} = z_{int,E} = z_{int,E'} = 0.459 +- 0.005 +- 0.025, where the first error bar represents statistical error (68% confidence interval) and the second error bar represents possible systematic error due to corrections to scaling (68% subjective confidence interval). For the "susceptibility-like" observables, we find z_{int,M^2} = z_{int,S_2} = 0.443 +- 0.005 +- 0.030. For the dynamic critical exponent associated to the exponential autocorrelation time, we find z_{exp} \approx 0.481. Our data are consistent with the Coddington-Baillie conjecture z_{SW} = \beta/\nu \approx 0.5183, especially if it is interpreted as referring to z_{exp}.Comment: LaTex2e, 39 pages including 5 figure