 94326 S. MiracleSole
 SURFACE TENSION, STEP FREE ENERGY AND FACETS IN THE EQUILIBRIUM CRYSTAL
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Oct 18, 94

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Abstract. Some aspects of the microscopic theory of interfaces
in classical lattice systems are developed. The problem
of the appearance of facets in the (Wulff) equilibrium
crystal shape is discussed, together with its relation
with the discontinuities of the derivatives of the surface
tension $\tau ({\bf n})$ (with respect to the components
of the surface normal ${\bf n}$) and the role of the step
free energy $\tau^{\rm step} ({\bf m})$ (associated to a
step orthogonal to ${\bf m}$ on a rigid interface). Among
the results are, in the case of the Ising model at low enough
temperatures, the existence of $\tau^{\rm step} ({\bf m})$
in the thermodynamic limit, the expression of this quantity
by means of a convergent cluster expansion, and the fact
that $2 \tau^{\rm step} ({\bf m})$ is equal to the value of
the jump of the derivative $\partial \tau / \partial \theta$
(when $\theta$ varies) at the point $\theta=0$ (with
${\bf n} = (m_1 \sin\theta, m_2 \sin\theta, \cos\theta)$).
Finally, using this fact, it is shown that the facet shape
is determined by the function $\tau^{\rm step} ({\bf m})$.
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