Double-exchange model in infinite dimension is studied as the strong Hund’s coupling limit J → ∞ of the Kondo lattice model. Several quantities such as Green’s function and the d.c. conductivity are calculated in analytical forms. Magnetoresistance in lightly doped La1−xSrxMnO3 is reproduced very well.

We consider a statistical mechanical model describing flux lines in type II superconductors by embedding the flux lines on a lattice wound on torus. The lines are nonintersecting and each loop of lines is associated with a fugacity z = -1. It is shown that the exact solution of this model leads to a second-order transition between the Meissner and the superconducting states as well as a first-o...

Several incidence theorems of planar projective geometry are considered. It is demonstrated that generalizations of Pascal theorem due to Möbius give rise to double cross-ratio equation and Hietarinta equation. The construction corresponding to the double cross-ratio equation is a reduction to a conic section of some planar configuration (203154). This configuration provides a correct definitio...

For a set X, let Σm(X) denote the set of metrizable topologies on X, partially ordered by inclusion. We investigate the nature of intervals in this partial order, with particular emphasis on basic intervals (in other words, intervals in which the topology changes at at most one point). We show that there are no non-trivial finite intervals in Σm(X) (indeed, every such interval contains a copy o...

We describe a recent program from the study of definable groups in certain o-minimal structures. A central notion of this program is that of a (geometric) lattice. We propose a definition of a lattice in an arbitrary first-order structure. We then use it to describe, uniformly, various structure theorems for o-minimal groups, each time recovering a lattice that captures some significant invaria...

An extended lattice model for reaction limited cluster-cluster aggregation is studied, where different kinds and states of bonds between monomers are considered. The decrease of the numbers of possible bonds per monomer yields decreasing fractal dimensions, which differ from the usual values obtained for diffusion limited and reaction limited clustercluster aggregation regimes, respectively.

A lattice model for four dimensional Euclidean quantum general relativity is proposed for a simplicial spacetime. It is shown how this model can be expressed in terms of a sum over worldsheets of spin networks in the lattice, and an interpretation of these worldsheets as spacetime geometries is given, based on the geometry defined by spin networks in canonical loop quantized GR. The spacetime g...

abstract. let $l$ be a lattice with the least element $0$. an element $xin l$ is a zero divisor if $xwedge y=0$ for some $yin l^*=lsetminus left{0right}$. the set of all zero divisors is denoted by $z(l)$. we associate a simple graph $gamma(l)$ to $l$ with vertex set $z(l)^*=z(l)setminus left{0right}$, the set of non-zero zero divisors of $l$ and distinct $x,yin z(l)^*$ are adjacent if and only...

Within the effective-field theory with correlations (EFT), a transverse random field spin-1 Ising model on the simple cubic (z=6) lattice is studied. The phase diagrams, the behavior of critical points, transverse magnetization,  internal energy, magnetic specific heat are obtained numerically and discussed for different values of p the concentration of the random transverse field.