Yes and no. Exemptions may include triplexes + multiunit structures built after 1978...if you file the right paperwork. Currently, when you lease an apartment in Santa Monica, your rent can be increased every September by an amount determined by the general assessment, which is announced in July.
As an FYI, the general assessment has yet to equal City of L.A.'s 4% annual rent increase allowance AND, it has never equalled the rate cost of living increase.
Beyond that, Santa Monica is a great place to live.