Nature of phase transition in magnetic thin films

We study the critical behavior of magnetic thin films as a function of the film thickness. We use the ferromagnetic Ising model with the high-resolution multiple histogram Monte Carlo (MC) simulation. We show that though the 2D behavior remains dominant at small thicknesses, there is a systematic continuous deviation of the critical exponents from their 2D values. We observe that in the same range of varying thickness the deviation of the exponent $\nu$ is very small from its 2D value, while exponent $\beta$ suffers a larger deviation. Moreover, as long as the film thickness is fixed, i. e. no finite size scaling is done in the $z$ direction perpendicular to the film, the 3D values of the critical exponents cannot be attained even with very large (but fixed) thickness. The crossover to 3D universality class cannot therefore take place without finite size scaling applied in the $z$ direction, in the limit of numerically accessible thicknesses. From values of exponent $\alpha$ obtained by MC, we estimate the effective dimension of the system. We conclude that with regard to the critical behavior, thin films behave as systems with effective dimension between 2 and 3.Comment: 8 pages, 17 figures, submitted to Phys. Rev.

Effect of Dipolar Interaction in Molecular Crystals

We investigate in this paper the ground state and the nature of the transition from an orientational ordered phase at low temperature to the disordered state at high temperature in a molecular crystal. Our model is a Potts model which takes into account the exchange interaction $J$ between nearest-neighbor molecules and a dipolar interaction between molecular axes in three dimensions. The dipolar interaction is characterized by two parameters: its amplitude $D$ and the cutoff distance $r_c$. If the molecular axis at a lattice site has three orientations, say the $x$, $y$ or $z$ axes, then when D=0, the system is equivalent to the 3-state Potts model: the transition to the disordered phase is known to be of first order. When $D\neq 0$, the ground-state configuration is shown to be composed of two independent interpenetrating layered subsystems which form a sandwich whose periodicity depends on $D$ and $r_c$. We show by extensive Monte Carlo simulation with a histogram method that the phase transition remains of first order at relatively large values of $r_c$.Comment: 6 pages, 7 figure