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We solve the monomer-dimer problem on a non-bipartite lattice, the simple quartic lattice with cylindrical boundary conditions, with a single monomer residing on the boundary. Due to the non-bipartite nature of the lattice, the well-known method of a Temperley bijection of solving single-monomer problems cannot be used. In this paper we derive the solution by mapping the problem onto one on close-packed dimers on a related lattice. Finite-size analysis of the solution is carried out. We find from asymptotic expansions of the free energy that the central charge in the logarithmic conformal field theory assumes the value $c=-2$.
An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be separable, w
We study a three species monomer-monomer catalytic surface reaction model with a reactive steady state bordered by three equivalent unreactive phases where the surface is saturated with one species. The transition from the reactive to a saturated pha
We study the number of dimer-monomers $M_d(n)$ on the Tower of Hanoi graphs $TH_d(n)$ at stage $n$ with dimension $d$ equal to 3 and 4. The entropy per site is defined as $z_{TH_d}=lim_{v to infty} ln M_d(n)/v$, where $v$ is the number of vertices on
We construct the Hamiltonian description of the Chern-Simons theory with Z_n gauge group on a triangular lattice. We show that the Z_2 model can be mapped onto free Majorana fermions and compute the excitation spectrum. In the bulk the spectrum turns
We present analytic results for a special dimer model on the {em non-bipartite} and {em non-planar} checkerboard lattice that does not allow for parallel dimers surrounding diagonal links. We {em exactly} calculate the number of closed packed dimer c