A family of novel models of liquid on a 2D lattice (2D lattice liquid models)
have been proposed as primitive models of soft-material membrane. As a first
step, we have formulated them as single-component, single-layered, classical
particle systems on a two-dimensional surface with no explicit viscosity. Among
the family of the models, we have shown and constructed two stochastic models,
a vicious walk model and a flow model, on an isotropic regular lattice and on
the rectangular honeycomb lattice of various sizes. In both cases, the dynamics
is governed by the nature of the frustration of the particle movements. By
simulations, we have found the approximate functional form of the frustration
probability, and peculiar anomalous diffusions in their time-averaged mean
square displacements in the flow model. The relations to other existing
statistical models and possible extensions of the models are also discussed.Comment: REVTeX4, 14 pages in double colomn, 12 figures; added references with
some comments, typos fixe