Finite-size Nagle-Kardar model: Casimir force

Abstract

We derive exact results for the critical Casimir force (CCF) within the Nagle-Kardar model with periodic boundary conditions (PBC's). The model represents one-dimensional Ising chain with long-range equivalent-neighbor ferromagnetic interactions of strength $J_l/N>0$ superimposed on the nearest-neighbor interactions of strength $J_s$ which could be either ferromagnetic ($J_s>0$) or antiferromagnetic ($J_s<0$). In the infinite system limit the model exhibits in the plane $(K_s=\beta J_s,K_l=\beta J_l)$ a critical line $2K_l=\exp \left(-2K_s\right),K_s>-\ln 3/4$, which ends at a tricritical point $(K_l=-\sqrt{3}/2,K_s=-\ln 3/4)$. The critical Casimir amplitudes are: ${\Delta }_{\mathrm{Cas}}^{(\mathrm{cr})}=1/4$ at the critical line, and ${\Delta }_{\mathrm{Cas}}^{(\mathrm{tr})}=1/3$ at the tricritical point. Quite unexpectedly, with the imposed PBC's the CCF exhibits very unusual behavior as a function of temperature and magnetic field. It is \textit{repulsive} near the critical line and tricritical point, decaying rapidly with separation from those two singular regimes fast away from them and becoming \textit{attractive}, displaying in which the maximum amplitude of the attraction exceeds the maximum amplitude of repulsion. This represents a violation of the widely-accepted ``boundary condition rule,'' which holds that the CCF is attractive for equivalent BC's and repulsive for conflicting BC's \textit{independently} of the actual bulk universality class of the phase transition under investigation.

6 pages, 3 figures; to appear in PRE as a letter

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Cited by in corpus (1)

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