Every wall needs a water-resistive barrier, thick insulation, and one or more air barriers
In general, exterior above-grade walls should have continuous air, water, and thermal barriers.
Installing rigid insulation as the exterior sheathingMaterial, usually plywood or oriented strand board (OSB), but sometimes wooden boards, installed on the exterior of wall studs, rafters, or roof trusses; siding or roofing installed on the sheathing—sometimes over strapping to create a rainscreen. can accomplish all of these tasks, but you need to account for shear resistance (provide wall bracing) in other ways, and you must provide special details if you expect the foam sheathing to perform as a water-resistive barrier (WRB).
A double-stud wallConstruction system in which two layers of studs are used to provide a thicker-than-normal wall system so that a lot of insulation can be installed; the two walls are often separated by several inches to reduce thermal bridging through the studs and to provide additional space for insulation. insulated with dense-packed cellulose is an excellent thermal barrier; however, double-stud walls still need at least one additional air barrier to limit air leakage through the cellulose.
Check out the advanced framing section of Construction Detail Library for alternative techniques to achieve shear resistance, and check out Using Rigid Foam As a Water-Resistive Barrier for more information on walls without housewrap.
For more information on air barriers, see Questions and Answers About Air Barriers