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The European Physical Journal B

Tricritical phase transitions in semi-infinite systems

W. Speth

Published Dec 1, 1983• 17 citations
Publisher
DOI
10.1007/bf01319219

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Phase transitions of the three-dimensional semi-infinite Blume-Emery-Griffiths model, extended to negative biquadratic interactions, are investigated within the framework of the mean-field approximation in comparison with the real-space renormalization-group results found previously. All the possible qualitative types of phase diagrams characterizing phase transitions of the model, including high entropy ferrimagnetic and staggered quadrupolar phases, have been determined. It is shown that such a system can exhibit critical and tricritical behavior on the surface and multicritical points.
We investigated a three-dimensional semi-infinite spin-1/2 system bounded by a spin-1 surface using a Monte Carlo simulation based on the Metropolis algorithm. The exchange interactions and crystal field effects on phase diagrams, magnetizations, and susceptibilities were investigated. The phase diagrams in three planes were presented due to the competition between specific system parameters. The system demonstrated ordinary, extraordinary, surface, and special second-order phase transitions, as well as a surface first-order phase transition. Furthermore, tricritical and critical end-points were discovered.
Abstract The Migdal–Kadanoff renormalization group technique is applied to study a three-dimensional semi-infinite Ising system consisting of spin-1/2 sites in the bulk and spin-1 sites at the surface. According to the competition ratio between bulk and surface exchange interactions ( R = J B / J S ), two types of surface phase diagrams have been identified in the (surface crystal field, temperature) plane. These diagrams exhibit a rich variety of phase transition phenomena: surface, ordinary, extraordinary, and special second-order transitions, first-order transitions at the surface, as well as tricritical and multicritical points. Additionally, we list in a table the fixed points that govern the observed phases and phase transitions.