The fall in melting point as a particle shrinks is explained by the Gibbs-Thomson effect, which relates the melting temperature of a small particle to its curvature and surface energy.

The physics is a surface-to-volume argument. In a nanoparticle a large fraction of the atoms sit on the surface, where they have fewer neighbours and therefore weaker binding than atoms in the bulk. Less thermal energy is needed to break them free, so the melting temperature falls, and the depression grows roughly in inverse proportion to the particle radius. Gold, which melts near 1064 °C in bulk, melts several hundred degrees lower as a few-nanometre particle.

The other effects describe different phenomena. The Casimir effect is an attraction between closely spaced uncharged plates arising from quantum vacuum fluctuations, the Seebeck effect is the generation of a voltage across a temperature gradient, and the Hall-Petch effect describes how strength increases as grain size decreases.

Hence, the answer is the Gibbs-Thomson effect.