相关论文: Dimer Statistics on a Bethe Lattice

The monomer-dimer model is fundamental in statistical mechanics. However, it is $#P$-complete in computation, even for two dimensional problems. A formulation in matrix permanent for the partition function of the monomer-dimer model is…

We express the finite 3D Dimer partition function as a linear combination of determinants of oriented adjacency matrices, and the finite 3D Ising partition sum as a linear combination of products over aperiodic closed walks. The methodology…

We introduce a lattice model for a static and isotropic system of relativistic fermions. An action principle is formulated, which describes a particle-particle interaction of all fermions. The model is designed specifically for a numerical…

So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking…

We develop a diagrammatic approach for solving few-body problems in heteronuclear fermionic mixtures near a narrow interspecies Feshbach resonance. We calculate s-, p-, and d-wave phaseshifts for the scattering of an atom by a weakly-bound…

We present a geometrical approach for studying dimers. We introduce a connection for dimer problems on bipartite and non-bipartite graphs. In the bipartite case the connection is flat but has non-trivial ${\bf Z}_2$ holonomy round certain…

By means of contact-density chain-growth simulations, we investigate a simple lattice model of a flexible polymer interacting with an attractive substrate. The contact density is a function of the numbers of monomer-substrate and…

The nested algebraic Bethe ansatz is presented for the anisotropic supersymmetric $U$ model maintaining quantum supersymmetry. The Bethe ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for…

We use a simple lattice statistical model to analyze the effects of directional interactions on the phase diagram of a fluid of two-state Janus particles. The problem is formulated in terms of nonlinear recursion relations along the…

Lattice models with non-hermitian, parity and time-reversal ($\mathcal{PT}$) symmetric Hamiltonians, realized most readily in coupled optical systems, have been intensely studied in the past few years. A $\mathcal{PT}$-symmetric dimer…

The mean square end-to-end distance of a N-step polymer on a Bethe lattice is calculated. We consider semiflexible polymers placed on isotropic and anisotropic lattices. The distance on the Cayley tree is defined by embedding the tree on a…

Lipid monolayers and bilayers have been used as experimental models for the investigation of membrane thermal transitions. The main transition takes place near ambient temperatures for several lipids and reflects the order-disorder…

A seminal milestone in lattice statistics is the exact solution of the enumeration of dimers on a simple-quartic net obtained by Fisher,Kasteleyn, and Temperley (FKT) in 1961. An outstanding related and yet unsolved problem is the…

There are few exactly solvable lattice models and even fewer solvable quantum lattice models. Here we address the problem of finding the spectrum of the tight-binding model (equivalently, the spectrum of the adjacency matrix) on Cayley…

This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The method is constructive and is easy to use. It is based upon the observation that…

The spinless fermion model with hard core repulsive potential extended on a few lattice sites is considered.The Luttinger liquid behaviour is studied for the different values of a hard core radius. A critical exponent of the one particle…

We report the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arrangements of particles in experiments in which…

Simple cubic lattice (SC lattice) can be viewed as plane triangular lattice (PT lattice) by viewing it along its principle diagonal lines. By viewing thus we establish the exact one-to-one correspondence between the closed graphs on SC…

We review some surprising links which have been discovered in the last few years between the theory of certain ordinary differential equations, and particular integrable lattice models and quantum field theories in two dimensions. An…

Mixed-spin Ising model on a decorated Bethe lattice is rigorously solved by combining the decoration-iteration transformation with the method of exact recursion relations. Exact results for critical lines, compensation temperatures, total…