6533b825fe1ef96bd12826d7
RESEARCH PRODUCT
Monte Carlo studies of finite-size effects at first-order transitions
Kurt BinderDavid P. LandauM. S. S. Challasubject
PhysicsCanonical ensemblePhase transitionMonte Carlo methodsymbols.namesakeDistribution functionThermodynamic limitsymbolsGeneral Materials ScienceIsing modelStatistical physicsvan der Waals forceInstrumentationPotts modeldescription
Abstract First-order phase transitions are ubiquitous in nature but their presence is often uncertain because of the effects which finite size has on all transitions. In this article we consider a general treatment of size effects on lattice systems with discrete degrees of freedom and which undergo a first-order transition in the thermodynamic limit. We review recent work involving studies of the distribution functions of the magnetization and energy at a first-order transition in a finite sample of size N connected to a bath of size N′. Two cases: N′ = ∞ and N′ = finite are considered. In the former (canonical ensemble) case, the distributions are approximated by a superposition of Gaussians corresponding to the different phases; all finite-size effects then vary as N or 1/N. The latter case involves the Gaussian ensemble where the entropy of the bath has a convenient form; for small N′, first-order transitions are characterized by van der Waals' loops in (for example) the energy vs. temperature curves....
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1990-08-01 | Phase Transitions |