Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this problem considerably for normal surfaces, by reducing the dimension of this vector space from 7n to 3n (where n is the complexity of the underlyi...

Orderly arrayed granular crystals exhibit extraordinary capability to tune stress wave propagation. Granular system of higher dimension renders many more stress wave patterns, showing its great potential for physical and engineering applications. At nanoscale, one-dimensionally arranged buckyball (C60) system has shown the ability to support solitary wave. In this paper, stress wave behaviors o...

The tetrahedron equation is a three-dimensional generalization of the Yang-Baxter equation. Its solutions define integrable three-dimensional lattice models of statistical mechanics and quantum field theory. Their integrability is not related to the size of the lattice, therefore the same solution of the tetrahedron equation defines different integrable models for different finite periodic cubi...

Sr_{2}CuTeO_{6} presents an opportunity for exploring low-dimensional magnetism on a square lattice of S=1/2  Cu^{2+} ions. We employ ab initio multireference configuration interaction calculations to unravel the Cu^{2+} electronic structure and to evaluate exchange interactions in Sr_{2}CuTeO_{6}. The latter results are validated by inelastic neutron scattering using linear spin-wave theory an...

The title compound, {[Cu(C(17)H(11)N(2)O(3))(2)(H(2)O)]·2H(2)O}(n), is a two-dimensional polymer. The Cu(2+) ion lies on the crystallographic twofold axis. The coordination sphere of the Cu(2+) ion can be described as a distorted square pyramid. All of the H atoms in the amide group and lattice water mol-ecules participate in O-H⋯O or N-H⋯O hydrogen bonding to strengthen the two-dimensioal fram...

We present a simple and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three examples: the two-dimensional three-state Potts antiferromagnet on the square lattice, and the two-dimensional O(3) and O(~) cr models. In favorable cases it ...

In this chapter we will be considering the effect of confining polygons to lie in a bounded geometry. This has already been briefly discussed in Chapters 2 and 3, but here we give many more results. The simplest, non-trivial case is that of SAP on the two-dimensional square lattice Z2, confined between two parallel lines, say x = 0 and x = w. This problem is essentially 1-dimensional, and as su...

After briefly describing the present status of the spin glass theory, we present a conjecture on the exact location of the multicritical point in the phase diagram of finite-dimensional spin glasses. The theory enables us to understand in a unified way many numerical results for two-, threeand four-dimensional models including the ±J Ising model, random Potts model, random lattice gauge theory,...

We study the superfluid to Mott-insulator transition of bosons in an optical anizotropic lattice by employing the Bose-Hubbard model living on a two-dimensional lattice with anizotropy parameter κ. The compressible superfluid state and incompressible Mott-insulator (MI) lobes are efficiently described analytically, using the quantum U(1) rotor approach. The ground state phase diagram showing th...

Using systematic effective field theory, we explore the properties of antiferromagnetic films subjected to magnetic and staggered fields that are either mutually aligned or orthogonal. We provide low-temperature series for entropy density in case up two-loop order. Invoking staggered, uniform sublattice magnetizations bipartite antiferromagnet, investigate subtle order-disorder phenomena spin a...