Thermodynamic Casimir effect for films in the 3D Ising universality class: Symmetry breaking boundary conditions

TL;DR

This study investigates the thermodynamic Casimir force in the 3D Ising universality class with symmetry breaking boundary conditions using Monte Carlo simulations of the improved Blume-Capel model, confirming theoretical predictions and comparing with previous results.

Contribution

The paper provides the first detailed Monte Carlo analysis of the Casimir force with symmetry breaking boundary conditions in the 3D Ising universality class, accounting for boundary-induced corrections to scaling.

Findings

Effective boundary correction length L_s=1.9(1) was determined.

Finite size scaling functions for the Casimir force were successfully collapsed across different film thicknesses.

Results agree with previous Monte Carlo, field theory, and experimental data.

Abstract

We study the thermodynamic Casimir force for films in the three-dimensional Ising universality class with symmetry breaking boundary conditions. To this end we simulate the improved Blume-Capel model on the simple cubic lattice. We study the two cases ++, where all spins at the boundary are fixed to +1 and +-, where the spins at one boundary are fixed to +1 while those at the other boundary are fixed to -1. An important issue in analyzing Monte Carlo and experimental data are corrections to scaling. Since we simulate an improved model, leading corrections to scaling, which are proportional to L_0^-omega, where L_0 is the thickness of the film and omega approx 0.8, can be ignored. This allows us to focus on corrections to scaling that are caused by the boundary conditions. We confirm the theoretical expectation that these corrections can be accounted for by an effective thickness L_0,eff = L_0 + L_s. Studying the correlation length of the films, the energy per area, the magnetization profile and the thermodynamic Casimir force at the bulk critical point we find L_s=1.9(1) for our model and the boundary conditions discussed here. Using this result for L_s we find a nice collapse of the finite size scaling curves obtained for the thicknesses L_0=8.5, 16.5 and 32.5 for the full range of temperatures that we consider. We compare our results for the finite size scaling functions theta_++ and theta_+- of the thermodynamic Casimir force with those obtained in a previous Monte Carlo study, by the de Gennes-Fisher local-functional method, field theoretic methods and an experiment with a binary mixture.