Monte Carlo Study of Order-Disorder Layering Transitions in the Blume-Capel Model

TL;DR

This study uses Monte Carlo simulations to analyze order-disorder layering transitions in the Blume-Capel model, revealing phase transition lines, tri-critical points, and reentrant phenomena influenced by temperature and layered magnetic fields.

Contribution

It provides new insights into the layering transitions, including the connection between first and second order lines and the reentrant phenomena caused by competing effects.

Findings

Identification of first and second order transition lines connected by tri-critical points.

Observation of reentrant phenomena in the first few layers due to thermal and magnetic field competition.

Analysis of layer-specific magnetizations and susceptibilities, including critical exponents.

Abstract

The order-disorder layering transitions, of the Blume-Capel model, are studied using the Monte Carlo (MC) simulations, in the presence of a variable crystal field. For a very low temperature, the results are in good agreement with the ground state study. The first order transition line, found for low temperatures, is connected to the second order transition line, seen for higher temperatures, by a tri-critical point, for each layer. The reentrant phenomena, caused by a competition of thermal fluctuations and an inductor magnetic field created by the deeper layers, is found for the first $k_0$ layers from the surface, where $k_0$ is exactly the number of layering transitions allowed by the ground state study. The layer magnetizations $m_k$, the magnetic susceptibilities $\chi_{m,k}$ and the quadrupolar magnetic susceptibilities $\chi_{q,k}$ and the corresponding critical exponent, for each layer $k$, are also investigated.