Interfaces and the Question of Regional Congruence in Spin Glasses

We present a general theorem restricting properties of interfaces between thermodynamic states and apply it to the spin glass excitations observed numerically by Krzakala and Martin and separately by Palassini and Young in spatial dimensions $d=3,4\mathrm{}$. We show that such excitations, with interface dimension $d_s<d$, cannot yield regionally congruent thermodynamic states. More generally, zero density interfaces of translation-covariant excitations cannot be pinned (by the disorder) in any $d$ but rather must deflect to infinity in the thermodynamic limit. Additional consequences concerning regional congruence in spin glasses and other systems are discussed.