A Monte Carlo study of surface critical phenomena: The special point

TL;DR

This study uses Monte Carlo simulations to precisely determine surface critical exponents at the special point in the phase diagram of three-dimensional Ising-like systems, comparing different models and boundary conditions.

Contribution

It provides accurate estimates of surface renormalization group exponents at the special point for the improved Blume-Capel and spin-1/2 Ising models, enhancing understanding of surface critical phenomena.

Findings

Estimated surface exponents: y_{t_s}=0.718(2), y_{h_s}=1.6465(6)

Compared results with field theoretic and Monte Carlo data

Analyzed surface transition behavior near the special point

Abstract

We study the special point in the phase diagram of a semi-infinite system, where the bulk transition is in the three-dimensional Ising universality class. To this end we perform a finite size scaling study of the improved Blume-Capel model on the simple cubic lattice with two different types of surface interactions. In order to check for the effect of leading bulk corrections we have also simulated the spin-1/2 Ising model on the simple cubic lattice. We have accurately estimated the surface enhancement coupling at the special point of these models. We find $y_{t_s}=0.718(2)$ and $y_{h_s}=1.6465(6)$ for the surface renormalization group exponents of the special transitions. These results are compared with previous ones obtained by using field theoretic methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore we study the behaviour of the surface transition near the special point and finally we discuss films with special boundary conditions at one surface and fixed ones at the other.