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The monomer-dimer problem and moment Lyapunov exponents of homogeneous Gaussian random fieldsстатья
Информация о цитировании статьи получена из
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 19 сентября 2015 г.
- Автор: Vladimirov I.G.
- Журнал: Discrete and Continuous Dynamical Systems - Series B
- Том: 18
- Номер: 2
- Год издания: 2013
- Издательство: American Institute of Mathematical Sciences
- Местоположение издательства: United States
- Первая страница: 575
- Последняя страница: 600
- DOI: 10.3934/dcdsb.2013.18.575
- Аннотация: 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.
- Добавил в систему: Владимиров Игорь Геннадиевич