Learn English – Cold containers don’t sweat—what do they do

In warm, humid climates: If you take a container of something (say, a can of Coke or a jar of mayonnaise) and leave it at room temperature, the outside becomes wet with droplets of water— sometimes **dripping wet*.

I have heard this called sweating. However, knowing something about how water vapor works, I know that this is not sweating; you might say it is the reverse of sweating.

I know the water that forms is called condensation, because water vapor has been cooled enough to make it condense out of the air.

But I wonder how one could most concisely describe what the can or jar is "doing" (verb) to get that way, or to describe the state (adjective) of the container after this has happened. Do I have to say something like
"It attracts condensation. " ?
or
"It becomes wet. "?

Airplane wings are said to ice up when it is cold enough to that ice forms.

But I never heard watering up (except as an expression for crying); I have heard tearing up which is based on intransitive tearing
http://i.word.com/idictionary/tear .
But none of these is an accurate metaphor for what the container does, as the moisture comes from outside, not inside.

So it seems the sweating and tearing metaphors harken back to a time when hydrology was misunderstood

I don't mean dew, which is formed as the ambient air gradually cools to the dew point; I mean the water that forms when warm air encounters a cooled object. Other objects don't get wet; only the cold one.

Nor do I mean fog up, which as far as I know is used only in reference to glass surfaces (e.g. eyeglasses or a mirror" becoming covered with such tiny droplets that they become difficult or impossible to see "through".

Is there some single word, phrasal verb or set phrase to refer to this common phenomenon accurately?