Analyticity of the off-axis string tension and the restoration of rotational symmetry in lattice systems

Abstract

In the body-centered solid-on-solid model of fluctuating lattice strings it has been proved rigorously that the heavy-quark potential obtained from off-axis strings is an analytic function of the coupling constant for $0<g<\ensuremath{\infty}$. This observation gives additional credence to the recent suggestion that off-axis strings evade the roughening transition and should be useful in lattice-gauge-theory calculations of the heavy-quark potential. The restoration of rotational symmetry in various lattice spin systems is studied to clarify analogous calculations done with the fluctuating string. Model calculations show that the restoration occurs gradually as the bulk critical point is approached and no structural phase transitions or nonanalyticities are encountered.