A variety of structural transitions in nature do not involve a group-subgroup relationship. A two-dimensional example is the transition between a square lattice and a triangular lattice, which is known to occur in vortex lattices, Wigner crystals, skyrmion lattices, colloids, diblock copolymers, etc. A three-dimensional analog is the shock-induced BCC to HCP transition in iron. We develop a sys...

Small changes in an external parameter can often lead to dramatic qualitative changes in the lowest energy quantum mechanical ground state of a correlated electron system. In anisotropic crystals, such as the high-temperature superconductors where electron motion occurs primarily on a two-dimensional square lattice, the quantum critical point between two such lowest energy states has nontrivial...

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.

The phase diagram of a vertex model introduced by P. Di Francesco (Nucl. Phys. B 525, 507 1998) representing the configurations of a square lattice which can fold with different bending energies along the main axes and the diagonals has been studied by Cluster Variation Method. A very rich structure with partially and completely folded phases, different disordered phases and a flat phase is fou...

We construct super Yang-Mills theories with N = 2, 4 supersymmetries on the two-dimensional square lattice keeping one or two supercharges exactly. Along the same line as the previous paper [1], the construction is based on topological field theory formulation. We present two kinds of modifications of the action which preserve the exact supersymmetry and resolve the problem of degenerate classi...

We present the results of an exact diagonalization study of the spin-1/2 Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore lattice, also known as the square lattice with crossings or the checkerboard lattice. Examining the low energy spectra for systems of up to 24 spins, we find that all clusters studied have non-degenerate ground states with total spin zero, and big en...

and analogous bounds are established here for odd lattices satisfying certain technical conditions (which are trivial for N=1 and 2). For N>1 in (V), lattices meeting the new bound are constructed that are analogous to the ``shorter'' and ``odd'' Leech lattices. These include an odd associate of the 16-dimensional Barnes Wall lattice and shorter and odd associates of the Coxeter Todd lattice. A...

Two dimensional N = ∞ chiral models on the square and honeycomb lattices are investigated by a strong coupling analysis. Strong coupling expansion turns out to be predictive for the evaluation of continuum physical quantities, to the point of showing asymptotic scaling. Indeed in the strong coupling region a quite large range of β values exists where the fundamental mass agrees, within about 5%...

Percolation is the study of connectedness in a randomly-chosen subset of an infinite graph. Following Grimmett[4], we set up percolation on a square lattice. We establish the existence of a critical edge-density, prove several results about the behavior of percolation systems above and below this critical density, and use these results to find the critical density of percolation on the two-dime...

The Mn(III) atom in the title complex, [Mn(C(18)H(18)N(2)O(4))(CHO(2))(H(2)O)]·2H(2)O, is O,N,N',O'-chelated by the deproton-ated Schiff base; the four chelating atoms form an approximate square, with the O atoms of the water mol-ecule and the formate ion in axial positions above and below the square plane. Two metal-bearing mol-ecules are linked by an O-H(water)⋯O hydrogen bond about a center ...