155 research outputs found
Thermodynamic Casimir effect: Universality and Corrections to Scaling
We study the thermodynamic Casimir force for films in the three-dimensional
Ising universality class with symmetry breaking boundary conditions. We focus
on the effect of corrections to scaling and probe numerically the universality
of our results. In particular we check our hypothesis that corrections are well
described by an effective thickness L_{0,eff}=L_0+c (L_0+L_s)^{1-\omega} +L_s,
where c and L_s are system specific parameters and \omega\approx 0.8 is the
exponent of the leading bulk correction. We simulate the improved Blume-Capel
model and the Ising model on the simple cubic lattice. First we analyse the
behaviour of various quantities at the critical point. Taking into account
corrections \propto L_0^{-\omega} in the case of the Ising model, we find good
consistency of results obtained from these two different models. In particular
we get from the analysis of our data for the Ising model for the difference of
Casimir amplitudes \Delta_{+-}-\Delta_{++}=3.200(5), which nicely compares with
\Delta_{+-}-\Delta_{++}=3.208(5) obtained by studying the improved Blume-Capel
model. Next we study the behaviour of the thermodynamic Casimir force for large
values of the scaling variable x=t [L_0/\xi_0]. This behaviour can be obtained
up to an overall amplitude by expressing the partition function of the film in
terms of eigenvalues and eigenstates of the transfermatrix and boundary states.
Here we show how this overall amplitude can be computed with high accuracy.
Finally we discuss our results for the scaling functions \theta_{+-} and
\theta_{++} of the thermodynamic Casimir force for the whole range of the
scaling variable. We conclude that our numerical results are in accordance with
universality. Corrections to scaling are well approximated by an effective
thickness.Comment: 35 pages, 5 figures, various typos correcte
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