Non-universal size dependence of the free energy of confined systems near criticality

Abstract

The singular part of the finite-size free energy density $f_s$ of the O(n) symmetric ${\varphi }^4$ field theory in the large-n limit is calculated at finite cutoff for confined geometries of linear size L with periodic boundary conditions in 2 < d < 4 dimensions. We find that a sharp cutoff $\Lambda$ causes a non-universal leading size dependence $f_s\sim {\Lambda }^{d-2}{L}^{-2}$ near $T_c$ which dominates the universal scaling term $\sim L^{-d}$. This implies a non-universal critical Casimir effect at $T_c$ and a leading non-scaling term $\sim L^{-2}$ of the finite-size specific heat above $T_c$.

RevTex, 4 pages

References in corpus (1)

• Two-point correlation function in systems with van der Waals type interaction

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