Violation of finite-size scaling for the free energy near criticality

Details Violation of finite-size scaling for the free energy near criticality Violation of finite-size scaling for the free energy near criticality

2001-12-17

arxiv.org/abs/cond-mat/0112310v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, no figure

Scientific paper

The singular part of the finite-size free energy density $f_s$ of the O($n$) symmetric $\phi^4$ field theory is calculated for confined geometries of linear size L with periodic boundary conditions in the large-N limit and with Dirichlet boundary conditions in one-loop order. We find that both a sharp cutoff and a subleading long-range interaction cause a non-universal L dependence of $f_s$ near $T_c$. For film geometry this implies a non-universal critical Casimir force with an algebraic L dependence that dominates the exponential finite-size scaling behavior above $T_c$ for both periodic and Dirichlet boundary conditions.

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