Is there a tensionless Kardar-Parisi-Zhang universality class above one dimension? An Ising model approach

The Kardar-Parisi-Zhang (KPZ) equation is a paradigm of generic scale invariance, for which it represents a conspicuous universality class. Recently, the tensionless case of this equation has been shown to provide a different universality class by itself. This class describes the -- intrinsically anomalous -- scaling of one-dimensional (1D) fronts for several physical systems that feature ballistic dynamics. In this work, we show that the evolution of certain 1D fronts defined for a 2D Ising system also belongs to the tensionless KPZ universality class. Nevertheless, the Ising fronts exhibit multiscaling, at variance with the continuous equation. The discrete nature of these fronts provides an alternative approach to assess the dynamics for the 2D front case (for a 3D Ising system), since the direct integration of the tensionless KPZ equation blows up in this case. In spite of the agreement between the 1D scaling of the Ising fronts and the tensionless KPZ equation, the fluctuation statistics in 1D and the full behavior in 2D are strongly conditioned by boundary effects.Comment: 9 pages, 9 figure