arXiv subjects

V. Popkov

Publications and source records attributed to V. Popkov.

21 records · Page 2Linked to original sources

arXiv1997

Lattice Statistics in Three Dimensions: Exact Solution of Layered Dimer and Layered Domain Wall Models

Exact analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer interactions. We show that both models are equivalent to a 5-vertex model on the square lattice with interlayer vertex-vertex interactions. Using the method of Bethe ansatz, a closed-form expression for the free energy is obtained and analyzed. We deduce the exact phase diagram and determine the nature of the phase transitions as a function of the strength of the interlayer interaction.

cond-mat.stat-mech↗

arXiv1996

3-Dimensional Multilayered 6-vertex Statistical Model: Exact Solution

Solvable via Bethe Ansatz (BA) anisotropic statistical model on cubic lattice consisting of locally interacting 6-vertex planes, is studied. Symmetries of BA lead to infinite hierarchy of possible phases, which is further restricted by numerical simulations. The model is solved for arbitrary value of the interlayer coupling constant. Resulting is the phase diagram in general 3-parameter space. Exact mapping onto the models with some inhomogenious sets of interlayer coupling constants is established.

cond-mat.stat-mech↗

arXiv1996

Exact Solution of a Three-Dimensional Dimer System

We consider a three-dimensional lattice model consisting of layers of vertex models coupled with interlayer interactions. For a particular non-trivial interlayer interaction between charge-conserving vertex models and using a transfer matrix approach, we show that the eigenvalues and eigenvectors of the transfer matrix are related to those of the two-dimensional vertex model. The result is applied to analyze the phase transitions in a realistic three-dimensional dimer system.

cond-mat.stat-mech↗