Size-driven dimensional crossover in the quasi-two-dimensional Ising model

We have studied the finite size effect in the quasi-two-dimensional Ising model by using a Monte Carlo simulation. A marked finite size effect was found with decreasing interlayer interaction. Aside from the well-known three- to two-dimensional crossover, a three- to one-dimensional crossover at a crossover size Lc∼(λ/2)−ν/φ was revealed as an origin of the marked finite size effect, where λ is the interlayer to intralayer interaction ratio, and ν and φ are the critical exponent for the correlation length and the crossover exponent, respectively. While the former crossover is driven by temperature, the latter is driven by size at a fixed λ.