Legendre transforms on a triangular lattice

Inverse Transforms of Products of Legendre Transforms

is obtained by applying successive integration by parts to the integral represented by the left-hand member of this equation so that the new integrand is the product of F by [(1 —x2)P„' ]', and by replacing this second factor by — n(n + l)Pn according to Legendre's differential equation [l]. Thus certain boundary value problems in ordinary and partial differential equations that involve the dif...

Apery Sequences and Legendre Transforms

A lower bound for the minimal length of the polynomial recurrence of a binomial sum is obtained. 2000 Mathematics subject classification: primary 11B37. A sequence an satisfies a polynomial recurrence of length r and degree m if there exist r polynomials Po, Pu ... , Pr_u with degree at most m such that (1) Po(n)an + P x { n ) a n ^ + ••• + P r ^ ( n ) a n r = 0 for n > r. For a sequence an the...

Dimer model on a triangular lattice.

We analyze the partition function of the dimer model on an M×N triangular lattice wrapped on a torus obtained by Fendley, Moessner, and Sondhi [Phys. Rev. B 66, 214513 (2002)]. From a finite-size analysis we have found that the dimer model on such a lattice can be described by a conformal field theory having a central charge c=-2. The shift exponent for the specific heat is found to depend on t...

Directed Percolation on a 2D Triangular Lattice

We study directed percolation on a 2D triangular lattice where the forward direction is perpendicular to one of the lattice axes. In addition to the geometrical description, an equivalent dynamic description of the model is presented. Simulations are performed based on an algorithm from the dynamic description to obtain the critical probability of bond occupation as pc ≈ 0.522. A mean field the...

Heisenberg Antiferromagnet on a Triangular Lattice