6533b862fe1ef96bd12c6e2f
RESEARCH PRODUCT
Surface tension and interfacial fluctuations in d-dimensional Ising model
J. Kaupužssubject
PhysicsStatistical Mechanics (cond-mat.stat-mech)Analytic continuationFOS: Physical sciencesGeneral Physics and AstronomyStatistical and Nonlinear PhysicsFractal dimensionComputer Science ApplicationsSurface tensionComputational Theory and MathematicsIsing modelHypercubeStatistical physicsScalingCritical exponentMathematical PhysicsCondensed Matter - Statistical MechanicsCurse of dimensionalitydescription
The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarised in a formula, which allows to interpolate the corrections to finite-size scaling between two and three dimensions. The physical meaning of an analytic continuation to noninteger values of the spatial dimensionality d is discussed. Lattices and interfaces with properly defined fractal dimensions should fulfil certain requirements to possibly have properties of an analytic continuation from d-dimensional hypercubes. Here 2 appears as the marginal value of d below which the (d-1)-dimensional interface splits in disconnected pieces. Some phenomenological arguments are proposed to describe such interfaces. They show that the character of the interfacial fluctuations at d<2 is not the same as provided by a formal analytic continuation from d-dimensional hypercubes with d >= 2. It, probably, is true also for the related critical exponents.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-01-04 |