  Polarity fields are known to exhibit long distance patterns, in both physical
and biological systems. The mechanisms behind such patterns are poorly
understood. Here, we describe the dynamics of polarity fields using an original
physical model that generalizes classical spin models on a lattice by
incorporating effective transport of polarity molecules between neighboring
sites. We account for an external field and for ferromagnetic interactions
between sites and prescribe the time-evolution of the system using two distinct
dissipative classes for non-conserved and conserved variables representing
polarity orientation and magnitude, respectively. We observe two main types of
steady-state configurations --disordered configurations and patterns of highly
polar spots surrounded by regions with low polarity-- and we characterise
patterns and transitions between configurations. Our results may provide
alternative pattern-generating mechanisms for materials endowed with polarity
fields.
