A novel exponent in the Equilibrium Shape of Crystals

TL;DR

This paper introduces a new exponent that describes the rounding of crystal facets by mapping crystal surfaces to the six-vertex model and applying the Bethe Ansatz, providing insights into critical behavior.

Contribution

It identifies a novel exponent in the equilibrium shape of crystals through a mapping to the six-vertex model and Bethe Ansatz analysis, extending understanding of crystal facet rounding.

Findings

Derived the new exponent characterizing facet rounding

Determined leading order exponents along phase boundaries

Discussed potential experimental verification

Abstract

A new exponent characterizing the rounding of crystal facets is found by mapping a crystal surface onto the asymmetric six-vertex model (i.e. with external fields h and v) and using the Bethe Ansatz to obtain appropriate expansions of the free energy close to criticality. Leading order exponents in \delta h, \delta v are determined along the whole phase boundary and in an arbitrary direction. A possible experimental verification of this result is discussed.