The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields

Details The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields

2012-04-07

arxiv.org/abs/1204.1674v1

Mathematics

Probability

24 pages, 4 figures, submitted on 14 October 2011 to a special issue of DCDS-B

Scientific paper

We consider an "elastic" version of the statistical mechanical monomer-dimer problem on the n-dimensional integer lattice. Our setting includes the classical "rigid" formulation as a special case and extends it by allowing each dimer to consist of particles at arbitrarily distant sites of the lattice, with the energy of interaction between the particles in a dimer depending on their relative position. We reduce the free energy of the elastic dimer-monomer (EDM) system per lattice site in the thermodynamic limit to the moment Lyapunov exponent (MLE) of a homogeneous Gaussian random field (GRF) whose mean value and covariance function are the Boltzmann factors associated with the monomer energy and dimer potential. In particular, the classical monomer-dimer problem becomes related to the MLE of a moving average GRF. We outline an approach to recursive computation of the partition function for "Manhattan" EDM systems where the dimer potential is a weighted l1-distance and the auxiliary GRF is a Markov random field of Pickard type which behaves in space like autoregressive processes do in time. For one-dimensional Manhattan EDM systems, we compute the MLE of the resulting Gaussian Markov chain as the largest eigenvalue of a compact transfer operator on a Hilbert space which is related to the annihilation and creation operators of the quantum harmonic oscillator and also recast it as the eigenvalue problem for a pantograph functional-differential equation.

Affiliated with

Also associated with

No associations

Rating

The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-37446