The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results

Details The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results

2004-02-09

arxiv.org/abs/cond-mat/0402238v1

Phys.Rev. E69 (2004) 046119

Physics

Condensed Matter

Statistical Mechanics

21 pages, 7 figures, to appear in PRE

Scientific paper

10.1103/PhysRevE.69.046119

We present general arguments and construct a stress tensor operator for finite lattice spin models. The average value of this operator gives the Casimir force of the system close to the bulk critical temperature $T_c$. We verify our arguments via exact results for the force in the two-dimensional Ising model, $d$-dimensional Gaussian and mean spherical model with $2=k_b T_c (d-1)\Delta/(L/a)^{d}$, where $L$ is the distance between the plates and $\Delta$ is the (universal) Casimir amplitude.

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